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| versions
list | update_date
timestamp[s] | authors_parsed
list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
quant-ph/9912092
|
S. A. Gardiner
|
S.A. Gardiner, D. Jaksch, R. Dum, J.I. Cirac, and P. Zoller
|
Nonlinear Matter Wave Dynamics with a Chaotic Potential
|
20 pages text, 20 gzipped ps and eps figures
|
Phys. Rev. A 62, 023612 (2000).
|
10.1103/PhysRevA.62.023612
| null |
quant-ph cond-mat
| null |
We consider the case of a cubic nonlinear Schr\"{o}dinger equation with an
additional chaotic potential, in the sense that such a potential produces
chaotic dynamics in classical mechanics. We derive and describe an appropriate
semiclassical limit to such a nonlinear Schr\"{o}dinger equation, using a
semiclassical interpretation of the Wigner function, and relate this to the
hydrodynamic limit of the Gross-Pitaevskii equation used in the context of
Bose-Einstein condensation. We investigate a specific example of a
Gross-Pitaevskii equation with such a chaotic potential: the one-dimensional
delta-kicked harmonic oscillator, and its semiclassical limit. We explore the
feasibility of experimental realization of such a system in a Bose-Einstein
condensate experiment, giving a concrete proposal of how to implement such a
configuration, and considering the problem of condensate depletion.
|
[
{
"version": "v1",
"created": "Mon, 20 Dec 1999 17:32:49 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Gardiner",
"S. A.",
""
],
[
"Jaksch",
"D.",
""
],
[
"Dum",
"R.",
""
],
[
"Cirac",
"J. I.",
""
],
[
"Zoller",
"P.",
""
]
] |
quant-ph/9912093
|
Jiannis Pachos
|
Jiannis Pachos and Spiros Chountasis (ISI)
|
Optical Holonomic Quantum Computer
|
16 pages, 3 figures, REVTEX
|
Phys.Rev.A62:052318,2000
|
10.1103/PhysRevA.62.052318
| null |
quant-ph hep-th physics.optics
| null |
In this paper the idea of holonomic quantum computation is realized within
quantum optics. In a non-linear Kerr medium the degenerate states of laser
beams are interpreted as qubits. Displacing devices, squeezing devices and
interferometers provide the classical control parameter space where the
adiabatic loops are performed. This results into logical gates acting on the
states of the combined degenerate subspaces of the lasers, producing any one
qubit rotations and interactions between any two qubits. Issues such as
universality, complexity and scalability are addressed and several steps are
taken towards the physical implementation of this model.
|
[
{
"version": "v1",
"created": "Mon, 20 Dec 1999 22:12:15 GMT"
}
] | 2008-12-18T00:00:00 |
[
[
"Pachos",
"Jiannis",
"",
"ISI"
],
[
"Chountasis",
"Spiros",
"",
"ISI"
]
] |
quant-ph/9912094
|
Krzysztof Kowalski
|
K. Kowalski and J. Rembielinski
|
Coherent states for a particle on a sphere
|
LaTeX, 16 pages, 2 figures
|
J.Phys.A33:6035-6048,2000
|
10.1088/0305-4470/33/34/309
| null |
quant-ph hep-th math-ph math.MP
| null |
The coherent states for a particle on a sphere are introduced. These states
are labelled by points of the classical phase space, that is the position on
the sphere and the angular momentum of a particle. As with the coherent states
for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J.
Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space
related with quantum fluctuations. The expectation values of the position and
the angular momentum in the coherent states are regarded as the best possible
approximation of the classical phase space. The correctness of the introduced
coherent states is illustrated by an example of the rotator.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 11:57:20 GMT"
}
] | 2008-11-26T00:00:00 |
[
[
"Kowalski",
"K.",
""
],
[
"Rembielinski",
"J.",
""
]
] |
quant-ph/9912095
|
J. F. Corney
|
P. D. Drummond and J. F. Corney
|
Quantum noise in optical fibers I: stochastic equations
|
1 figure
| null | null | null |
quant-ph
| null |
We analyze the quantum dynamics of radiation propagating in a single mode
optical fiber with dispersion, nonlinearity, and Raman coupling to thermal
phonons. We start from a fundamental Hamiltonian that includes the principal
known nonlinear effects and quantum noise sources, including linear gain and
loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are
treated. This allows quantum Langevin equations to be calculated, which have a
classical form except for additional quantum noise terms. In practical
calculations, it is more useful to transform to Wigner or +$P$
quasi-probability operator representations. These result in stochastic
equations that can be analyzed using perturbation theory or exact numerical
techniques. The results have applications to fiber optics communications,
networking, and sensor technology.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 14:21:53 GMT"
},
{
"version": "v2",
"created": "Mon, 28 Aug 2000 13:06:47 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Drummond",
"P. D.",
""
],
[
"Corney",
"J. F.",
""
]
] |
quant-ph/9912096
|
J. F. Corney
|
J. F. Corney and P. D. Drummond
|
Quantum noise in optical fibers II: Raman jitter in soliton
communications
|
3 figures
| null | null | null |
quant-ph
| null |
The dynamics of a soliton propagating in a single-mode optical fiber with
gain, loss, and Raman coupling to thermal phonons is analyzed. Using both
soliton perturbation theory and exact numerical techniques, we predict that
intrinsic thermal quantum noise from the phonon reservoirs is a larger source
of jitter and other perturbations than the gain-related Gordon-Haus noise, for
short pulses, assuming typical fiber parameters. The size of the Raman timing
jitter is evaluated for both bright and dark (topological) solitons, and is
larger for bright solitons. Because Raman thermal quantum noise is a nonlinear,
multiplicative noise source, these effects are stronger for the more intense
pulses needed to propagate as solitons in the short-pulse regime. Thus Raman
noise may place additional limitations on fiber-optical communications and
networking using ultrafast (subpicosecond) pulses.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 14:17:29 GMT"
},
{
"version": "v2",
"created": "Mon, 28 Aug 2000 13:17:21 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Corney",
"J. F.",
""
],
[
"Drummond",
"P. D.",
""
]
] |
quant-ph/9912097
|
Stefano Giovanazzi
|
D. O'Dell (1), S. Giovanazzi (1), G. Kurizki (1), V. M. Akulin (2)
((1) Weizmann Institute of Science, (2) Laboratoire Aime' Cotton)
|
Bose Condensates with 1/r Interatomic Attraction: Electromagnetically
Induced ``Gravity''
|
4 pages, 2 figures
|
Phys. Rev. Lett. 84, 5687 (2000)
|
10.1103/PhysRevLett.84.5687
| null |
quant-ph cond-mat
| null |
We show that particular configurations of intense off-resonant laser beams
can give rise to an attractive 1/r interatomic potential between atoms located
well within the laser wavelength. Such a ``gravitational-like'' interaction is
shown to give stable Bose condensates that are self-bound (without an
additional trap) with unique scaling properties and measurably distinct
signatures.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 15:48:28 GMT"
}
] | 2011-06-09T00:00:00 |
[
[
"O'Dell",
"D.",
"",
"Weizmann Institute of Science"
],
[
"Giovanazzi",
"S.",
"",
"Weizmann Institute of Science"
],
[
"Kurizki",
"G.",
"",
"Weizmann Institute of Science"
],
[
"Akulin",
"V. M.",
"",
"Laboratoire Aime' Cotton"
]
] |
quant-ph/9912098
|
Michal Horodecki
|
Piotr Badziag, Michal Horodecki, Pawel Horodecki, and Ryszard
Horodecki
|
Local environment can enhance fidelity of quantum teleportation
|
9 pages, Revtex
| null |
10.1103/PhysRevA.62.012311
| null |
quant-ph
| null |
We show how an interaction with the environment can enhance fidelity of
quantum teleportation. To this end, we present examples of states which cannot
be made useful for teleportation by any local unitary transformations;
nevertheless, after being subjected to a dissipative interaction with the local
environment, the states allow for teleportation with genuinely quantum
fidelity. The surprising fact here is that the necessary interaction does not
require any intelligent action from the parties sharing the states. In passing,
we produce some general results regarding optimization of teleportation
fidelity by local action. We show that bistochastic processes cannot improve
fidelity of two-qubit states. We also show that in order to have their fidelity
improvable by a local process, the bipartite states must violate the so-called
reduction criterion of separability.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 19:02:12 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Badziag",
"Piotr",
""
],
[
"Horodecki",
"Michal",
""
],
[
"Horodecki",
"Pawel",
""
],
[
"Horodecki",
"Ryszard",
""
]
] |
quant-ph/9912099
|
George Svetlichny
|
George Svetlichny (Pontificia Universidade Catolica, Rio de Janeiro,
Brazil)
|
The Space-time Origin of Quantum Mechanics: Covering Law
|
LaTeX, 37 pages
|
Found.Phys. 30 (2000) 1819-1847
| null | null |
quant-ph gr-qc
| null |
Lorentz covariance imposed upon a quantum logic of local propositions for
which all observers can consistently maintain state collapse descriptions,
implies a condition on space-like separated propositions that if imposed on
generally commuting ones would lead to the covering law, and hence to a
hilbert-space model for the logic. Such a generalization can be argued if state
preparation can be conditioned to space-like separated events using EPR-type
correlations. This suggests that the covering law is related to space-time
structure, though a final understanding of it, through a self-consistency
requirement, will probably require quantum space-time.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 20:16:31 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Svetlichny",
"George",
"",
"Pontificia Universidade Catolica, Rio de Janeiro,\n Brazil"
]
] |
quant-ph/9912100
|
Igor V. Volovich
|
Masanori Ohya and Igor V. Volovich
|
Quantum Computing, NP-complete Problems and Chaotic Dynamics
|
11 pages, 1 figure
| null | null | null |
quant-ph chao-dyn cond-mat.mes-hall cs.CC nlin.CD physics.atom-ph
| null |
An approach to the solution of NP-complete problems based on quantum
computing and chaotic dynamics is proposed. We consider the satisfiability
problem and argue that the problem, in principle, can be solved in polynomial
time if we combine the quantum computer with the chaotic dynamics amplifier
based on the logistic map. We discuss a possible implementation of such a
chaotic quantum computation by using the atomic quantum computer with quantum
gates described by the Hartree-Fock equations. In this case, in principle, one
can build not only standard linear quantum gates but also nonlinear gates and
moreover they obey to Fermi statistics. This new type of entaglement related
with Fermi statistics can be interesting also for quantum communication theory.
|
[
{
"version": "v1",
"created": "Tue, 21 Dec 1999 22:03:01 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Ohya",
"Masanori",
""
],
[
"Volovich",
"Igor V.",
""
]
] |
quant-ph/9912101
|
Robert J. C. Spreeuw
|
D. Voigt, B.T. Wolschrijn, R. Jansen, N. Bhattacharya, R.J.C. Spreeuw,
and H.B. van Linden van den Heuvell
|
Observation of radiation pressure exerted by evanescent waves
|
6 pages, 4 figures
|
Phys. Rev. A 61, 063412 (2000)
|
10.1103/PhysRevA.61.063412
| null |
quant-ph
| null |
We report a direct observation of radiation pressure, exerted on cold
rubidium atoms while bouncing on an evanescent-wave atom mirror. We analyze the
radiation pressure by imaging the motion of the atoms after the bounce. The
number of absorbed photons is measured for laser detunings ranging from {190
MHz} to {1.4 GHz} and for angles from {0.9 mrad} to {24 mrad} above the
critical angle of total internal reflection. Depending on these settings, we
find velocity changes parallel with the mirror surface, ranging from 1 to {18
cm/s}. This corresponds to 2 to 31 photon recoils per atom. These results are
independent of the evanescent-wave optical power.
|
[
{
"version": "v1",
"created": "Wed, 22 Dec 1999 09:40:52 GMT"
},
{
"version": "v2",
"created": "Thu, 10 Feb 2000 13:58:55 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Voigt",
"D.",
""
],
[
"Wolschrijn",
"B. T.",
""
],
[
"Jansen",
"R.",
""
],
[
"Bhattacharya",
"N.",
""
],
[
"Spreeuw",
"R. J. C.",
""
],
[
"Heuvell",
"H. B. van Linden van den",
""
]
] |
quant-ph/9912102
|
M. Czachor
|
Marek Czachor
|
Field quantization by means of a single harmonic oscillator
| null | null | null | null |
quant-ph
| null |
A new scheme of field quantization is proposed. Instead of associating with
different frequencies different oscillators we begin with a single oscillator
that can exist in a superposition of different frequencies. The idea is applied
to the electromagnetic radiation field. Using the standard Dirac-type
mode-quantization of the electromagnetic field we obtain several standard
properties such as coherent states or spontaneous and stimulated emission. As
opposed to the standard approach the vacuum energy is finite and does not have
to be removed by any ad hoc procedure.
|
[
{
"version": "v1",
"created": "Wed, 22 Dec 1999 15:39:41 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Czachor",
"Marek",
""
]
] |
quant-ph/9912103
|
Dr. PETZ Denes
|
D. Petz and M. Mosonyi
|
Stationary quantum source coding
|
8 pages
|
J. Math. Phys. 42(2001), 4857-4864
|
10.1063/1.1398335
| null |
quant-ph
| null |
In this paper the quantum source coding theorem is obtained for a completely
ergodic source. This results extends Shannon's classical theorem as well as
Schumacher's quantum noiseless coding theorem for memoryless sources. The
control of the memory effects requires earlier results of Hiai and Petz on high
probability subspaces.
|
[
{
"version": "v1",
"created": "Wed, 22 Dec 1999 17:22:22 GMT"
},
{
"version": "v2",
"created": "Fri, 9 Mar 2001 16:00:44 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Petz",
"D.",
""
],
[
"Mosonyi",
"M.",
""
]
] |
quant-ph/9912104
|
Jeff P. Barnes
|
Jeff P Barnes, Warren S Warren
|
Automatic Quantum Error Correction
|
16 pages 12 fig LaTex uses multicol, graphicx expanded version of
letter submitted to Phys Rev Lett
| null |
10.1103/PhysRevLett.85.856
| null |
quant-ph
| null |
Criteria are given by which dissipative evolution can transfer populations
and coherences between quantum subspaces, without a loss of coherence. This
results in a form of quantum error correction that is implemented by the joint
evolution of a system and a cold bath. It requires no external intervention
and, in principal, no ancilla. An example of a system that protects a qubit
against spin-flip errors is proposed. It consists of three spin 1/2 magnetic
particles and three modes of a resonator. The qubit is the triple quantum
coherence of the spins, and the photons act as ancilla.
|
[
{
"version": "v1",
"created": "Wed, 22 Dec 1999 21:36:04 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Barnes",
"Jeff P",
""
],
[
"Warren",
"Warren S",
""
]
] |
quant-ph/9912105
|
Paul G. Kwiat
|
D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G.
Kwiat (Los Alamos National Laboratory, USA)
|
Entangled state quantum cryptography: Eavesdropping on the Ekert
protocol
|
4 pages, 2 encapsulated postscript files, PRL (tentatively) accepted
|
Physical Review Letters 84, 4733-4736 (2000).
|
10.1103/PhysRevLett.84.4733
|
LAUR-99-5760
|
quant-ph
| null |
Using polarization-entangled photons from spontaneous parametric
downconversion, we have implemented Ekert's quantum cryptography protocol. The
near-perfect correlations of the photons allow the sharing of a secret key
between two parties. The presence of an eavesdropper is continually checked by
measuring Bell's inequalities. We investigated several possible eavesdropper
strategies, including pseudo-quantum non-demolition measurements. In all cases,
the eavesdropper's presence was readily apparent. We discuss a procedure to
increase her detectability.
|
[
{
"version": "v1",
"created": "Thu, 23 Dec 1999 02:38:28 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Naik",
"D. S.",
"",
"Los Alamos National Laboratory, USA"
],
[
"Peterson",
"C. G.",
"",
"Los Alamos National Laboratory, USA"
],
[
"White",
"A. G.",
"",
"Los Alamos National Laboratory, USA"
],
[
"Berglund",
"A. J.",
"",
"Los Alamos National Laboratory, USA"
],
[
"Kwiat",
"P. G.",
"",
"Los Alamos National Laboratory, USA"
]
] |
quant-ph/9912106
|
Joerg Schmiedmayer
|
Ron Folman, Peter Kr\"uger, Donatella Cassettari, Bj\"orn Hessmo,
Thomas Maier, J\"org Schmiedmayer
|
Atom Chips
| null |
Phys. Rev. Lett. 84, 4749 (2000)
|
10.1103/PhysRevLett.84.4749
| null |
quant-ph
| null |
Atoms can be trapped and guided using nano-fabricated wires on surfaces,
achieving the scales required by quantum information proposals. These Atom
Chips form the basis for robust and widespread applications of cold atoms
ranging from atom optics to fundamental questions in mesoscopic physics, and
possibly quantum information systems.
|
[
{
"version": "v1",
"created": "Thu, 23 Dec 1999 14:55:04 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Folman",
"Ron",
""
],
[
"Krüger",
"Peter",
""
],
[
"Cassettari",
"Donatella",
""
],
[
"Hessmo",
"Björn",
""
],
[
"Maier",
"Thomas",
""
],
[
"Schmiedmayer",
"Jörg",
""
]
] |
quant-ph/9912107
|
Kurt Jacobs
|
Andrew C. Doherty, Salman Habib, Kurt Jacobs, Hideo Mabuchi, Sze M.
Tan
|
Quantum feedback control and classical control theory
|
14 pages, multicol revtex, 2 eps figures
|
Phys. Rev. A 62, 012105 (2000)
|
10.1103/PhysRevA.62.012105
| null |
quant-ph
| null |
We introduce and discuss the problem of quantum feedback control in the
context of established formulations of classical control theory, examining
conceptual analogies and essential differences. We describe the application of
state-observer based control laws, familiar in classical control theory, to
quantum systems and apply our methods to the particular case of switching the
state of a particle in a double-well potential.
|
[
{
"version": "v1",
"created": "Fri, 24 Dec 1999 19:25:05 GMT"
},
{
"version": "v2",
"created": "Thu, 9 Mar 2000 22:08:58 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Doherty",
"Andrew C.",
""
],
[
"Habib",
"Salman",
""
],
[
"Jacobs",
"Kurt",
""
],
[
"Mabuchi",
"Hideo",
""
],
[
"Tan",
"Sze M.",
""
]
] |
quant-ph/9912108
|
Robert Clifton
|
Rob Clifton (Department of Philosophy, University of Pittsburgh)
|
Complementarity between Position and Momentum as a Consequence of
Kochen-Specker Arguments
|
4 pages, LaTeX
| null |
10.1016/S0375-9601(00)00365-0
| null |
quant-ph
| null |
We give two simple Kochen-Specker arguments for complementary between the
position and momentum components of spinless particles, arguments that are
identical in structure to those given by Peres and Mermin for spin-1/2
particles.
|
[
{
"version": "v1",
"created": "Sun, 26 Dec 1999 01:47:22 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Clifton",
"Rob",
"",
"Department of Philosophy, University of Pittsburgh"
]
] |
quant-ph/9912109
|
Nakamura Etsuko
|
Ken-Ichi Aoki, Atsushi Horikoshi, and Etsuko Nakamura (Kanazawa
University)
|
Time of arrival through interacting environments: Tunneling processes
|
Latex 19 pages, 11 eps figures, title modified, comments and
references added, final version
|
Phys.Rev. A62 (2000) 22101
|
10.1103/PhysRevA.62.022101
|
KANAZAWA/99-14
|
quant-ph gr-qc
| null |
We discuss the propagation of wave packets through interacting environments.
Such environments generally modify the dispersion relation or shape of the wave
function. To study such effects in detail, we define the distribution function
P_{X}(T), which describes the arrival time T of a packet at a detector located
at point X. We calculate P_{X}(T) for wave packets traveling through a
tunneling barrier and find that our results actually explain recent
experiments. We compare our results with Nelson's stochastic interpretation of
quantum mechanics and resolve a paradox previously apparent in Nelson's
viewpoint about the tunneling time.
|
[
{
"version": "v1",
"created": "Sun, 26 Dec 1999 09:18:22 GMT"
},
{
"version": "v2",
"created": "Tue, 25 Jul 2000 08:41:42 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Aoki",
"Ken-Ichi",
"",
"Kanazawa\n University"
],
[
"Horikoshi",
"Atsushi",
"",
"Kanazawa\n University"
],
[
"Nakamura",
"Etsuko",
"",
"Kanazawa\n University"
]
] |
quant-ph/9912110
|
M. B. Miller
|
V.B. Belyaev (1), Yu.Z. Ionikh (2), M.B. Miller (3), A.K. Motovilov
(1), A.V. Sermyagin (3), A.A. Smolnikov (1,4), Yu.A. Tolmachev (2)((1) Joint
Institute for Nuclear Research, (2) Saint-Petersburg State University, (3)
Institute of Physical and Engineering Problems,(4) Institute for Nuclear
Research)
|
Experiments on Sonoluminescence: Possible Nuclear and QED Aspects and
Optical Applications
|
4 pages; to be published by AIP in the Proc. ISNA-15
|
AIP Conference Proceedings 524 (2000), 413-416
|
10.1063/1.1309253
| null |
quant-ph
| null |
Experiments aimed at testing some hypothesis about the nature of Single
Bubble Sonoluminescence are discussed. A possibility to search for micro-traces
of thermonuclear neutrons is analyzed, with the aid of original low-background
neutron counter operating under conditions of the deep shielding from Cosmic
and other sources of background. Besides, some signatures of QED-contribution
to the light emission in SBSL are under the consideration, as well as new
approaches to probe a temperature inside the bubble. An applied-physics portion
of the program is presented also, in which an attention is being paid to
single- and a few-pulse light sources on the basis of SBSL.
|
[
{
"version": "v1",
"created": "Sun, 26 Dec 1999 15:46:42 GMT"
}
] | 2007-07-16T00:00:00 |
[
[
"Belyaev",
"V. B.",
""
],
[
"Ionikh",
"Yu. Z.",
""
],
[
"Miller",
"M. B.",
""
],
[
"Motovilov",
"A. K.",
""
],
[
"Sermyagin",
"A. V.",
""
],
[
"Smolnikov",
"A. A.",
""
],
[
"Tolmachev",
"Yu. A.",
""
]
] |
quant-ph/9912111
|
Lavagno Andrea
|
A. Lavagno and P. Narayana Swamy
|
Thermostatistics of q-deformed boson gas
|
19 pages, 5 figures. To appear in Phys. Rev. E
|
Phys.Rev.E61:1218,2000
|
10.1103/PhysRevE.61.1218
| null |
quant-ph cond-mat.stat-mech nucl-th
| null |
We show that a natural realization of the thermostatistics of q-bosons can be
built on the formalism of q-calculus and that the entire structure of
thermodynamics is preserved if we use an appropriate Jackson derivative in
place of the ordinary thermodynamics derivative. This framework allows us to
obtain a generalized q-boson entropy which depends on the q-basic number. We
study the ideal q-boson gas in the thermodynamic limit which is shown to
exhibit Bose-Einstein condensation with higher critical temperature and
discontinuous specific heat.
|
[
{
"version": "v1",
"created": "Mon, 27 Dec 1999 10:42:29 GMT"
}
] | 2011-08-17T00:00:00 |
[
[
"Lavagno",
"A.",
""
],
[
"Swamy",
"P. Narayana",
""
]
] |
quant-ph/9912112
|
Supriyo Bandyopadhyay
|
Supriyo Bandyopadhyay
|
The Double Quantum Dot Feline Cousin of Schroedinger's Cat: An
Experimental Testbed for a Discourse of Quantum Measurement Dichotomies
|
7 pages, 1 figure
| null | null | null |
quant-ph
| null |
Intriguing dichotomies in quantum measurement theory involving the role of
the obersever, objective reality, collapse of wavefunctions and actualization
of a measurement outcome are cast into a patholigical gedanken experiment
involving a single electron in a double quantum dot system coupled via a weak
link.
|
[
{
"version": "v1",
"created": "Mon, 27 Dec 1999 19:46:48 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Bandyopadhyay",
"Supriyo",
""
]
] |
quant-ph/9912113
|
Victor Zadkov
|
B.A.Grishanin and V.N.Zadkov
|
Coherent information analysis of quantum channels in simple quantum
systems
|
24 pages, 7 figs; Final versiob after minor changes, title changed;
to be published in Phys. Rev. A, September 2000
|
Phys. Rev. A 62, 032303 (2000)
|
10.1103/PhysRevA.62.032303
| null |
quant-ph
| null |
The coherent information concept is used to analyze a variety of simple
quantum systems. Coherent information was calculated for the information decay
in a two-level atom in the presence of an external resonant field, for the
information exchange between two coupled two-level atoms, and for the
information transfer from a two-level atom to another atom and to a photon
field. The coherent information is shown to be equal to zero for all
full-measurement procedures, but it completely retains its original value for
quantum duplication. Transmission of information from one open subsystem to
another one in the entire closed system is analyzed to learn quantum
information about the forbidden atomic transition via a dipole active
transition of the same atom. It is argued that coherent information can be used
effectively to quantify the information channels in physical systems where
quantum coherence plays an important role.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 09:13:19 GMT"
},
{
"version": "v2",
"created": "Tue, 4 Jan 2000 15:54:55 GMT"
},
{
"version": "v3",
"created": "Thu, 15 Jun 2000 14:07:46 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Grishanin",
"B. A.",
""
],
[
"Zadkov",
"V. N.",
""
]
] |
quant-ph/9912114
|
Armin Uhlmann
|
Armin Uhlmann
|
"Partial" Fidelities
|
LATEX2e, 14 pages
|
Rep. Math. Phys. 45, 407-418 (2000)
|
10.1016/S0034-4877(00)80007-5
|
ESI preprint 810
|
quant-ph math-ph math.MP
| null |
For pairs, omega, rho, of density operators on a finite dimensional Hilbert
space of dimension d I call k-fidelity the d - k smallest eigenvalues of |
omega^1/2 rho^1/2 |. k-fidelities are jointly concave in omega, rho. This
follows by representing them as infima over linear functions. For k = 0 known
properties of fidelity and transition probability are reproduced. Partial
fidelities characterize equivalence classes which are partially ordered in a
natural way.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 10:00:03 GMT"
},
{
"version": "v2",
"created": "Mon, 27 Mar 2000 09:40:58 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Uhlmann",
"Armin",
""
]
] |
quant-ph/9912115
|
Krzysztof Kowalski
|
K. Kowalski and J. Rembielinski
|
The $\delta$-deformation of the Fock space
|
LaTeX, 13 pages
|
Acta Physica Polonica, 34 (2003) 45-58
| null | null |
quant-ph math-ph math.MP
| null |
A deformation of the Fock space based on the finite difference replacement
for the derivative is introduced. The deformation parameter is related to the
dimension of the finite analogue of the Fock space.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 14:17:43 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Kowalski",
"K.",
""
],
[
"Rembielinski",
"J.",
""
]
] |
quant-ph/9912116
|
Morton H. Rubin
|
Arthur O. Pittenger and Morton H. Rubin
|
Complete Separability and Fourier representations of n-qubit states
| null |
Phys. Rev. A62, 042306 (2000).
|
10.1103/PhysRevA.62.042306
| null |
quant-ph
| null |
Necessary conditions for separability are most easily expressed in the
computational basis, while sufficient conditions are most conveniently
expressed in the spin basis. We use the Hadamard matrix to define the
relationship between these two bases and to emphasize its interpretation as a
Fourier transform. We then prove a general sufficient condition for complete
separability in terms of the spin coefficients and give necessary and
sufficient conditions for the complete separability of a class of generalized
Werner densities. As a further application of the theory, we give necessary and
sufficient conditions for full separability for a particular set of $n$-qubit
states whose densities all satisfy the Peres condition.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 16:09:50 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Pittenger",
"Arthur O.",
""
],
[
"Rubin",
"Morton H.",
""
]
] |
quant-ph/9912117
|
Thomas Jennewein
|
Thomas Jennewein (1), Christoph Simon (1), Gregor Weihs (1), Harald
WeinfurterD (2), and Anton Zeilinger (1) ((1) University of Vienna, (2)
University of Munich)
|
Quantum Cryptography with Entangled Photons
|
4 pages, 3 figures (1 in color). Submitted to PRL
| null |
10.1103/PhysRevLett.84.4729
| null |
quant-ph
| null |
By realizing a quantum cryptography system based on polarization entangled
photon pairs we establish highly secure keys, because a single photon source is
approximated and the inherent randomness of quantum measurements is exploited.
We implement a novel key distribution scheme using Wigner's inequality to test
the security of the quantum channel, and, alternatively, realize a variant of
the BB84 protocol. Our system has two completely independent users separated by
360 m, and generates raw keys at rates of 400 - 800 bits/second with bit error
rates arround 3 percent.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 17:50:18 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Jennewein",
"Thomas",
""
],
[
"Simon",
"Christoph",
""
],
[
"Weihs",
"Gregor",
""
],
[
"WeinfurterD",
"Harald",
""
],
[
"Zeilinger",
"Anton",
""
]
] |
quant-ph/9912118
|
Thomas Jennewein
|
Thomas Jennewein (1), Ulrich Achleitner (2), Gregor Weihs (1), Harald
Weinfurter (3), Anton Zeilinger (1) ((1) University of Vienna, (2) University
of Innsbruck, (3) University of Munich)
|
A Fast and Compact Quantum Random Number Generator
|
23 pages, 6 Figs. To appear in Rev. Sci. Instr
| null |
10.1063/1.1150518
| null |
quant-ph
| null |
We present the realization of a physical quantum random number generator
based on the process of splitting a beam of photons on a beam splitter, a
quantum mechanical source of true randomness. By utilizing either a beam
splitter or a polarizing beam splitter, single photon detectors and high speed
electronics the presented devices are capable of generating a binary random
signal with an autocorrelation time of 11.8 ns and a continuous stream of
random numbers at a rate of 1 Mbit/s. The randomness of the generated signals
and numbers is shown by running a series of tests upon data samples. The
devices described in this paper are built into compact housings and are simple
to operate.
|
[
{
"version": "v1",
"created": "Tue, 28 Dec 1999 19:52:33 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Jennewein",
"Thomas",
""
],
[
"Achleitner",
"Ulrich",
""
],
[
"Weihs",
"Gregor",
""
],
[
"Weinfurter",
"Harald",
""
],
[
"Zeilinger",
"Anton",
""
]
] |
quant-ph/9912119
|
M. B. Miller
|
B.F. Kostenko, V.D. Kuznetsov, M.B. Miller, A.V. Sermyagin, and D.V.
Kamanin
|
Nuclear Teleportation
|
8 pages, 2 figures, to be submitted to the Third Israeli Conference
for Conveying and Handling of Particulate Solids, The Dead Sea, May 29 - June
1, 2000
| null | null | null |
quant-ph
| null |
Until recently, only science-fiction authors ventured to use a term
teleportation. However, in the last few years, on the eve of upcoming new
millennium, the situation changed very much. The present report gives a
synopsis of main concepts in this area. The readers will be able to make sure
that paradoxical phenomena in the microcosm give a possibility to demonstrate
the exchange of properties between microobjects, removed at a very large
distance from each other, when no forces act between them. A new experimental
scheme with hydrogen and helium nuclei is proposed. It is expected that the
results of these experiments will be considered as teleportation of nuclear
properties of atoms of the simplest chemical elements. A problem of
teleportation of the more palpable cargo is left to the physics of the more
distant future.
|
[
{
"version": "v1",
"created": "Thu, 30 Dec 1999 14:36:35 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Kostenko",
"B. F.",
""
],
[
"Kuznetsov",
"V. D.",
""
],
[
"Miller",
"M. B.",
""
],
[
"Sermyagin",
"A. V.",
""
],
[
"Kamanin",
"D. V.",
""
]
] |
quant-ph/9912120
|
Matteo Beccaria
|
Eleonora Alfinito and Giuseppe Vitiello
|
Life-time and hierarchy of memory in the dissipative quantum model of
brain
|
4pages, no figures, paper accepted for publication in the JCIS 2000
Proceedings
| null |
10.1142/S0217979200001734
| null |
quant-ph cond-mat nlin.AO physics.bio-ph q-bio
| null |
Some recent developments of the dissipative quantum model of brain are
reported. In particular, the time-dependent frequency case is considered with
its implications on the different life-times of the collective modes.
|
[
{
"version": "v1",
"created": "Thu, 30 Dec 1999 15:37:17 GMT"
}
] | 2009-10-31T00:00:00 |
[
[
"Alfinito",
"Eleonora",
""
],
[
"Vitiello",
"Giuseppe",
""
]
] |
quant-ph/9912121
|
James Franson
|
J. D. Franson, T. B. Pittman, and J. P. Dowling
|
Simple pulse sequence for quantum logic operations using photon-exchange
interactions
|
This paper has been withdrawn
| null | null | null |
quant-ph
| null |
This paper has been withdrawn by the authors due to an error first noted by
M. Lukin.
|
[
{
"version": "v1",
"created": "Thu, 30 Dec 1999 16:06:07 GMT"
},
{
"version": "v2",
"created": "Sun, 2 Jan 2000 18:33:14 GMT"
},
{
"version": "v3",
"created": "Thu, 2 Mar 2000 15:20:08 GMT"
},
{
"version": "v4",
"created": "Tue, 27 May 2003 19:23:55 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Franson",
"J. D.",
""
],
[
"Pittman",
"T. B.",
""
],
[
"Dowling",
"J. P.",
""
]
] |
quant-ph/9912122
|
Benjamin Schumacher
|
Benjamin Schumacher (Kenyon College) and Michael D. Westmoreland
(Denison University)
|
Optimal signal ensembles
|
12 pages, 1 eps figure
| null | null | null |
quant-ph
| null |
Classical messages can be sent via a noisy quantum channel in various ways,
corresponding to various choices of signal states of the channel. Previous work
by Holevo and by Schumacher and Westmoreland relates the capacity of the
channel to the properties of the signal ensemble. Here we describe some
properties characterizing the ensemble that maximizes the capacity, using the
relative entropy "distance" between density operators to give the results a
geometric flavor.
|
[
{
"version": "v1",
"created": "Fri, 31 Dec 1999 17:17:44 GMT"
}
] | 2007-05-23T00:00:00 |
[
[
"Schumacher",
"Benjamin",
"",
"Kenyon College"
],
[
"Westmoreland",
"Michael D.",
"",
"Denison University"
]
] |
quant-ph/9912123
| null |
Alexander R. Kessel and Vladimir L. Ermakov
|
Multilevel Quantum Particle as a Few Virtual Qubits Materialization
|
15 pages, PostScript, no figures; paper accepted for publication in
the Proceedings of the VIII International Readings On Quantum Optics (Kazan,
October 27-29, 1999, Russia)
|
Proc. of SPIE Vol. 4061, pp.68-78 (2000)
|
10.1117/12.375307
| null |
quant-ph
| null |
A conception of virtual quantum information bit - virtual qubit - is
introduced. It is shown by means of virtual qubit representation that four
states of a single quantum particle is enough for implementation of full set of
the gates, which is necessary for creation an arbitrary algorithm for a quantum
computer. The physical nature and mutual disposition of four working states is
of no significance, if there are suitable selection rules for the particle
interaction with the external electromagnetic field pulses.
|
[
{
"version": "v1",
"created": "Fri, 31 Dec 1999 20:42:22 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Kessel",
"Alexander R.",
""
],
[
"Ermakov",
"Vladimir L.",
""
]
] |
solv-int/9304001
|
Jarmo Hietarinta
|
Kenji Kajiwara (Department of Applied Physics, Faculty of Engineering,
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan) Yasuhiro Ohta
(Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606,
Japan) Junkichi Satsuma (Department of Mathematical Sciences, University of
Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan)
|
q-Discrete Toda Molecule Equation
|
12 pages in plain tex
| null |
10.1016/0375-9601(93)90705-5
| null |
solv-int hep-th nlin.SI
| null |
A q-discrete version of the two-dimensional Toda molecule equation is
proposed through the direct method. Its solution, B\"acklund transformation and
Lax pair are discussed. The reduction to the q-discrete cylindrical Toda
molecule equation is also discussed.
|
[
{
"version": "v1",
"created": "Fri, 16 Apr 1993 06:56:31 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Kajiwara",
"Kenji",
"",
"Department of Applied Physics, Faculty of Engineering,\n University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan"
],
[
"Ohta",
"Yasuhiro",
"",
"Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606,\n Japan"
],
[
"Satsuma",
"Junkichi",
"",
"Department of Mathematical Sciences, University of\n Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan"
]
] |
solv-int/9304002
|
Kaji
|
Yasuhiro Ohta (Research Institute for Mathematical Sciences, Kyoto
University, Kyoto 606, Japan) Kenji Kajiwara (Department of Applied Physics,
Faculty of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyu-ku, Tokyo
113, Japan) Junkichi Satsuma (Department of Mathematical Sciences, University
of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan)
|
Casorati Determinant Solution for the Relativistic Toda Lattice Equation
|
19 pages in plain Tex
| null |
10.1063/1.530298
| null |
solv-int nlin.SI
| null |
The relativistic Toda lattice equation is decomposed into three Toda systems,
the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete
time Toda lattice. It is shown that the solutions of the equation are given in
terms of the Casorati determinant. By using the Casoratian technique, the
bilinear equations of Toda systems are reduced to the Laplace expansion form
for determinants. The $N$-soliton solution is explicitly constructed in the
form of the Casorati determinant.
|
[
{
"version": "v1",
"created": "Thu, 22 Apr 1993 04:51:06 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Ohta",
"Yasuhiro",
"",
"Research Institute for Mathematical Sciences, Kyoto\n University, Kyoto 606, Japan"
],
[
"Kajiwara",
"Kenji",
"",
"Department of Applied Physics,\n Faculty of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyu-ku, Tokyo\n 113, Japan"
],
[
"Satsuma",
"Junkichi",
"",
"Department of Mathematical Sciences, University\n of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan"
]
] |
solv-int/9304003
|
Robert I. McLachlan
|
Robert I. McLachlan (Program in Applied Mathematics, University of
Colorado at Boulder)
|
Integrable four-dimensional symplectic maps of standard type
|
5 pages, compile with plain TEX. No figures. To appear in Physics
Letters A
| null |
10.1016/0375-9601(93)90027-W
| null |
solv-int nlin.SI
| null |
We search for rational, four-dimensional maps of standard type (x_{n+1} -
2x_n + x_{n-1} = eps f(x,eps)) possessing one or two polynomial integrals.
There are no non-trivial maps corresponding to cubic oscillators, but we find a
four-parameter family of such maps corresponding to quartic oscillators. This
seems to be the only such example.
|
[
{
"version": "v1",
"created": "Wed, 28 Apr 1993 19:58:33 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"McLachlan",
"Robert I.",
"",
"Program in Applied Mathematics, University of\n Colorado at Boulder"
]
] |
solv-int/9305001
| null |
Ziemowit Popowicz (Research Institute for Theoretical Physics,
Siltavuorenpenger 20C, Fin-00014 University of Helsinki Finland)
|
The Super W_3 Conformal Algebra and the Boussinesq Hierarchy
|
12 pages
| null |
10.1142/S0217751X94000844
| null |
solv-int nlin.SI
| null |
The bihamiltonian structure of the N=2 Supersymmetric Boussinesq equation is
found. It is not reduced to the corresponding classical structure and hence it
describes the pure supersymmetric effect. For the supersymmetric Boussinesq
equation which contains the classical partner the Lax pair is given
explicitely. Thus we prove the integrability of the equation.
|
[
{
"version": "v1",
"created": "Thu, 13 May 1993 13:20:09 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Popowicz",
"Ziemowit",
"",
"Research Institute for Theoretical Physics,\n Siltavuorenpenger 20C, Fin-00014 University of Helsinki Finland"
]
] |
solv-int/9305002
|
Jeremy Schiff
|
Jeremy Schiff
|
B\"acklund Transformations of MKdV and Painlev\'e Equations
|
8 pages, plain tex
| null |
10.1088/0951-7715/7/1/015
|
IASSNS-HEP-93/9
|
solv-int nlin.SI
| null |
For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of
the first nontrivial equation in the $SL(N) MKdV hierarchy, generalizing the
two $Z_2$ actions on the space of solutions of the standard MKdV equation.
These actions survive scaling reduction, and give rise to transformation groups
for certain (systems of) ODEs, including the second, fourth and fifth
Painlev\'e equations.
|
[
{
"version": "v1",
"created": "Wed, 19 May 1993 19:07:45 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Schiff",
"Jeremy",
""
]
] |
solv-int/9305003
|
Vladimir Makhankov
|
V.G. Makhankov (Center for Nonlinear Studies, LANL and Joint Institute
for Nuclear Research, LCTA, Dubna, Moscow, Russia)
|
On exact solution for some integrable nonlinear equations of the
Schr\"odinger type
|
LaTeX
| null | null |
LA-UR-93-1331
|
solv-int nlin.PS nlin.SI patt-sol
| null |
The outlook of a simple method to generate localized (soliton-like)
potentials of time-dependent Schrodinger type equations is given. The
conditions are discussed for the potentials to be real and nonsingular. For the
derivative Schrodinger equation also is discussed its relation to the
Ishimori-II model. Some pecular soliton solutions of nonlinear Schrodinger type
equations are given and discussed.
|
[
{
"version": "v1",
"created": "Fri, 28 May 1993 17:42:13 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Makhankov",
"V. G.",
"",
"Center for Nonlinear Studies, LANL and Joint Institute\n for Nuclear Research, LCTA, Dubna, Moscow, Russia"
]
] |
solv-int/9305004
|
Karen Chaltikian
|
Aleksander A. Belov and Karen D. Chaltikian
|
Lattice Virasoro from Lattice Kac-Moody
| null | null |
10.1016/0370-2693(93)91572-5
| null |
solv-int hep-th nlin.SI
| null |
A new version of quantum Miura transformation on the lattice is proposed,
based on the lattice Kac-Moody algebra. A possibility of existence of the
Sugawara construction on the lattice is discussed.
|
[
{
"version": "v1",
"created": "Mon, 31 May 1993 08:36:23 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Belov",
"Aleksander A.",
""
],
[
"Chaltikian",
"Karen D.",
""
]
] |
solv-int/9306001
|
Jarmo Hietarinta
|
Jarmo Hietarinta (Department of Physics, University of Turku, Finland)
|
The upper triangular solutions to the three-state constant quantum
Yang-Baxter equation
|
24 Pages in LaTeX
| null |
10.1088/0305-4470/26/23/044
| null |
solv-int hep-th nlin.SI
| null |
In this article we present all nonsingular upper triangular solutions to the
constant quantum Yang-Baxter equation
$R_{j_1j_2}^{k_1k_2}R_{k_1j_3}^{l_1k_3}R_{k_2k_3}^{l_2l_3}=
R_{j_2j_3}^{k_2k_3}R_{j_1k_3}^{k_1l_3}R_{k_1k_2}^{l_1l_2}$ in the three state
case, i.e. all indices ranging from 1 to 3. The upper triangular ansatz implies
729 equations for 45 variables. Fortunately many of the equations turned out to
be simple allowing us to start breaking the problem into smaller ones. In the
end we had a total of 552 solutions, but many of them were either inherited
from two-state solutions or subcases of others. The final list contains 35
nontrivial solutions, most of them new.
|
[
{
"version": "v1",
"created": "Mon, 14 Jun 1993 15:35:11 GMT"
},
{
"version": "v2",
"created": "Fri, 18 Jun 1993 01:45:45 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Hietarinta",
"Jarmo",
"",
"Department of Physics, University of Turku, Finland"
]
] |
solv-int/9306002
|
Peter Clarkson
|
Peter A. Clarkson and Elizabeth L. Mansfield (Department of
Mathematics, University of Exeter, Exeter, U.K. and Program in Applied
Mathematics, University of Colorado, Boulder, CO, U.S.A.)
|
Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat
Equations
|
Latex file 32 pages, 13 figures available from author
| null | null |
PAM #145
|
solv-int nlin.SI
| null |
Classical and nonclassical symmetries of the nonlinear heat equation
$$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential
Gr\"obner bases is used both to find the conditions on $f(u)$ under which
symmetries other than the trivial spatial and temporal translational symmetries
exist, and to solve the determining equations for the infinitesimals. A
catalogue of symmetry reductions is given including some new reductions for the
linear heat equation and a catalogue of exact solutions of (1) for cubic $f(u)$
in terms of the roots of $f(u)=0$.
|
[
{
"version": "v1",
"created": "Wed, 16 Jun 1993 19:02:15 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Clarkson",
"Peter A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K. and Program in Applied\n Mathematics, University of Colorado, Boulder, CO, U.S.A."
],
[
"Mansfield",
"Elizabeth L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K. and Program in Applied\n Mathematics, University of Colorado, Boulder, CO, U.S.A."
]
] |
solv-int/9306003
|
Robert I. McLachlan
|
Robert I. McLachlan and Harvey Segur (Program in Applied Mathematics,
University of Colorado at Boulder)
|
A note on the motion of surfaces
|
10 pages, compile with AMSTEX. Two figures available from the authors
| null |
10.1016/0375-9601(94)91278-5
|
Program in Applied Math preprint #162, submitted to J. Diff. Geom
|
solv-int nlin.SI
| null |
We study the motion of surfaces in an intrinsic formulation in which the
surface is described by its metric and curvature tensors. The evolution
equations for the six quantities contained in these tensors are reduced in
number in two cases: (i) for arbitrary surfaces, we use principal coordinates
to obtain two equations for the two principal curvatures, highlighting the
similarity with the equations of motion of a plane curve; and (ii) for surfaces
with spatially constant negative curvature, we use parameterization by
Tchebyshev nets to reduce to a single evolution equation. We also obtain
necessary and sufficient conditions for a surface to maintain spatially
constant negative curvature as it moves. One choice for the surface's normal
motion leads to the modified-Korteweg de Vries equation,the appearance of which
is explained by connections to the AKNS hierarchy and the motion of space
curves.
|
[
{
"version": "v1",
"created": "Wed, 23 Jun 1993 23:24:04 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"McLachlan",
"Robert I.",
"",
"Program in Applied Mathematics,\n University of Colorado at Boulder"
],
[
"Segur",
"Harvey",
"",
"Program in Applied Mathematics,\n University of Colorado at Boulder"
]
] |
solv-int/9306004
|
Marco Boiti
|
M. Boiti, F. Pempinelli (Dipartimento di Fisica dell'Universita` e
Sezione INFN, Lecce, Italy) and A. Pogrebkov (Steklov Mathematical Institute,
Moscow, Russia)
|
Solutions of the Kpi Equation with Smooth Initial Data
|
17 pages, 23 June 1993, LaTex file
| null |
10.1088/0266-5611/10/3/001
| null |
solv-int nlin.SI
| null |
The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with
given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No
additional special constraints, usually considered in literature, as
$\int\!dx\,u(0,x,y)=0$ are required to be satisfied by the initial data. The
problem is completely solved in the framework of the spectral transform theory
and it is shown that $u(t,x,y)$ satisfies a special evolution version of the
KPI equation and that, in general, $\partial_t u(t,x,y)$ has different left and
right limits at the initial time $t=0$. The conditions of the type
$\int\!dx\,u(t,x,y)=0$, $\int\!dx\,xu_y(t,x,y)=0$ and so on (first, second,
etc. `constraints') are dynamically generated by the evolution equation for
$t\not=0$. On the other side $\int\!dx\!\!\int\!dy\,u(t,x,y)$ with prescribed
order of integrations is not necessarily equal to zero and gives a nontrivial
integral of motion.
|
[
{
"version": "v1",
"created": "Wed, 30 Jun 1993 06:07:06 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Boiti",
"M.",
"",
"Dipartimento di Fisica dell'Universita` e\n Sezione INFN, Lecce, Italy"
],
[
"Pempinelli",
"F.",
"",
"Dipartimento di Fisica dell'Universita` e\n Sezione INFN, Lecce, Italy"
],
[
"Pogrebkov",
"A.",
"",
"Steklov Mathematical Institute,\n Moscow, Russia"
]
] |
solv-int/9310001
|
Jan Felipe v. Diejen
|
J. F. van Diejen
|
Deformations of Calogero-Moser Systems
|
4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli,
Italy
|
Theor Math.Phys.99:549-554,1994
|
10.1007/BF01016137
| null |
solv-int hep-th nlin.SI
| null |
Recent results are surveyed pertaining to the complete integrability of some
novel n-particle models in dimension one. These models generalize the
Calogero-Moser systems related to classical root systems. Quantization leads to
difference operators instead of differential operators.
|
[
{
"version": "v1",
"created": "Mon, 18 Oct 1993 12:17:51 GMT"
}
] | 2010-10-27T00:00:00 |
[
[
"van Diejen",
"J. F.",
""
]
] |
solv-int/9310002
|
Kaji
|
Kenji Kajiwara(Dept. Appl. Phys., Fac. Engin., Univ. of Tokyo, Japan),
Yasuhiro Ohta(RIMS, Kyoto Univ., Japan), Junkichi Satsuma(Dept. Math. Sci.,
Univ. of Tokyo, Japan), Basil Grammaticos(LPN, Univ. Paris VII, France), and
Alfred Ramani(CPT, Ecole Polytechnique, France)
|
Casorati Determinant Solutions for the Discrete Painlev\'e-II Equation
|
13 pages in plain TeX
| null |
10.1088/0305-4470/27/3/030
| null |
solv-int nlin.SI
| null |
We present a class of solutions to the discrete Painlev\'e-II equation for
particular values of its parameters. It is shown that these solutions can be
expressed in terms of Casorati determinants whose entries are discrete Airy
functions. The analogy between the $\tau$ function for the discrete P$_{\rm
\romanno2}$ and the that of the discrete Toda molecule equation is pointed out.
|
[
{
"version": "v1",
"created": "Wed, 20 Oct 1993 06:20:17 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Kajiwara",
"Kenji",
"",
"Dept. Appl. Phys., Fac. Engin., Univ. of Tokyo, Japan"
],
[
"Ohta",
"Yasuhiro",
"",
"RIMS, Kyoto Univ., Japan"
],
[
"Satsuma",
"Junkichi",
"",
"Dept. Math. Sci.,\n Univ. of Tokyo, Japan"
],
[
"Grammaticos",
"Basil",
"",
"LPN, Univ. Paris VII, France"
],
[
"Ramani",
"Alfred",
"",
"CPT, Ecole Polytechnique, France"
]
] |
solv-int/9310003
|
Basile Grammaticos
|
B. Grammaticos (LPN, Universit\'e Paris VII, Tour 24-14, 5 etage,
Paris, France), F.W. Nijhoff (Department of Mathematics and Computer Science,
Clarkson University, Potsdam NY, USA), V. Papageorgiou (LPN, Universit\'e
Paris VII Tour 24-14, 5 etage, Paris, France and Department of Mathematics
and Computer Science Clarkson University, Potsdam NY, USA) and A. Ramani
(CPT, Ecole Polytechnique CNRS, UPR 14, 91128 Palaiseau, France)
|
Linearization And Solutions Of The Discrete Painlev\'e-III Equation
| null | null |
10.1016/0375-9601(94)91124-X
| null |
solv-int nlin.SI
| null |
We present particular solutions of the discrete Painlev\'e III
(d-P$\rm_{III}$) equation of rational and special function (Bessel) type. These
solutions allow us to establish a close parallel between this discrete equation
and its continuous counterpart. Moreover, we propose an alternate form for
d-P$\rm_{III}$ and confirm its integrability by explicitly deriving its Lax
pair.
|
[
{
"version": "v1",
"created": "Wed, 3 Nov 1993 09:56:21 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Grammaticos",
"B.",
"",
"LPN, Université Paris VII, Tour 24-14, 5 etage,\n Paris, France"
],
[
"Nijhoff",
"F. W.",
"",
"Department of Mathematics and Computer Science,\n Clarkson University, Potsdam NY, USA"
],
[
"Papageorgiou",
"V.",
"",
"LPN, Université\n Paris VII Tour 24-14, 5 etage, Paris, France and Department of Mathematics\n and Computer Science Clarkson University, Potsdam NY, USA"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique CNRS, UPR 14, 91128 Palaiseau, France"
]
] |
solv-int/9311001
|
Jarmo Hietarinta
|
J. Hietarinta and A. Ramani (CPT, Ecole Polytechnique, Palaiseau,
France), and B. Grammaticos (LPN, Universite Paris VII, Paris, France)
|
Continuous vacua in bilinear soliton equations
|
9 pages in Latex + 3 figures (not included)
| null |
10.1088/0305-4470/27/9/027
| null |
solv-int nlin.SI
| null |
We discuss the freedom in the background field (vacuum) on top of which the
solitons are built. If the Hirota bilinear form of a soliton equation is given
by $A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0$ where both $A$
and $B$ are even polynomials in their variables, then there can be a continuum
of vacua, parametrized by a vacuum angle $\phi$. The ramifications of this
freedom on the construction of one- and two-soliton solutions are discussed. We
find, e.g., that once the angle $\phi$ is fixed and we choose $u=\arctan G/F$
as the physical quantity, then there are four different solitons (or kinks)
connecting the vacuum angles $\pm\phi$, $\pm\phi\pm\Pi2$ (defined modulo
$\pi$). The most interesting result is the existence of a ``ghost'' soliton; it
goes over to the vacuum in isolation, but interacts with ``normal'' solitons by
giving them a finite phase shift.
|
[
{
"version": "v1",
"created": "Wed, 24 Nov 1993 10:10:50 GMT"
}
] | 2009-10-22T00:00:00 |
[
[
"Hietarinta",
"J.",
"",
"CPT, Ecole Polytechnique, Palaiseau,\n France"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique, Palaiseau,\n France"
],
[
"Grammaticos",
"B.",
"",
"LPN, Universite Paris VII, Paris, France"
]
] |
solv-int/9401001
|
Ron Perline
|
Joel Langer (Case Western Reserve University), Ron Perline (Drexel
University)
|
Local Geometric Invariants of Integrable Evolution Equations
|
15 pages, AMSTeX file (to appear in Journal of Mathematical Physics)
| null |
10.1063/1.530567
| null |
solv-int nlin.SI
| null |
The integrable hierarchy of commuting vector fields for the localized
induction equation of 3D hydrodynamics, and its associated recursion operator,
are used to generate families of integrable evolution equations which preserve
local geometric invariants of the evolving curve or swept-out surface.
|
[
{
"version": "v1",
"created": "Thu, 6 Jan 1994 01:32:35 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Langer",
"Joel",
"",
"Case Western Reserve University"
],
[
"Perline",
"Ron",
"",
"Drexel\n University"
]
] |
solv-int/9401002
|
Dr "P. A" Clarkson
|
Peter A. Clarkson and Elizabeth L. Mansfield (Department of
Mathematics, University of Exeter, Exeter, U.K.)
|
Algorithms for the Nonclassical Method of Symmetry Reductions
|
Latex file 27 pages, 2 figures available from author
| null | null |
PAM #164, University of Colorado at Boulder
|
solv-int nlin.SI
| null |
In this article we present first an algorithm for calculating the determining
equations associated with so-called ``nonclassical method'' of symmetry
reductions (a la Bluman and Cole) for systems of partial differentail
equations. This algorithm requires significantly less computation time than
that standardly used, and avoids many of the difficulties commonly encountered.
The proof of correctness of the algorithm is a simple application of the theory
of Grobner bases. In the second part we demonstrate some algorithms which may
be used to analyse, and often to solve, the resulting systems of overdetermined
nonlinear PDEs. We take as our principal example a generalised Boussinesq
equation, which arises in shallow water theory. Although the equation appears
to be non-integrable, we obtain an exact ``two-soliton'' solution from a
nonclassical reduction.
|
[
{
"version": "v1",
"created": "Wed, 12 Jan 1994 17:32:39 GMT"
},
{
"version": "v2",
"created": "Thu, 13 Jan 1994 16:12:30 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Clarkson",
"Peter A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Mansfield",
"Elizabeth L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
]
] |
solv-int/9401003
|
Dr "P. A" Clarkson
|
Peter A. Clarkson and Elizabeth L. Mansfield (Department of
Mathematics, University of Exeter, Exeter,U.K.)
|
On a Shallow Water Wave Equation
|
Tex file 21 pages, 15 figures available from author
| null |
10.1088/0951-7715/7/3/012
|
PAM #171, University of Colorado at Boulder
|
solv-int nlin.PS nlin.SI patt-sol
| null |
In this paper we study a shallow water equation derivable using the
Boussinesq approximation, which includes as two special cases, one equation
discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one
by Hirota and Satsuma [J. Phys. Soc. Japan}, 40 (1976) 611--612]. A catalogue
of classical and nonclassical symmetry reductions, and a Painleve analysis, are
given. Of particular interest are families of solutions found containing a rich
variety of qualitative behaviours. Indeed we exhibit and plot a wide variety of
solutions all of which look like a two-soliton for t>0 but differ radically for
t<0. These families arise as nonclassical symmetry reduction solutions and
solutions found using the singular manifold method. This example shows that
nonclassical symmetries and the singular manifold method do not, in general,
yield the same solution set. We also obtain symmetry reductions of the shallow
water equation solvable in terms of solutions of the first, third and fifth
Painleve equations. We give evidence that the variety of solutions found which
exhibit ``nonlinear superposition'' is not an artefact of the equation being
linearisable since the equation is solvable by inverse scattering. These
solutions have important implications with regard to the numerical analysis for
the shallow water equation we study, which would not be able to distinguish the
solutions in an initial value problem since an exponentially small change in
the initial conditions can result in completely different qualitative
behaviours.
|
[
{
"version": "v1",
"created": "Thu, 13 Jan 1994 16:13:33 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Clarkson",
"Peter A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter,U.K."
],
[
"Mansfield",
"Elizabeth L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter,U.K."
]
] |
solv-int/9401004
|
Leon Jerome
|
Jerome Leon
|
Nonlinear integrable systems related to arbitrary space-time dependence
of the spectral transform
|
27 pages, Latex file, Submitted to Journ Math Phys
| null |
10.1063/1.530426
|
PM94/01 Phys. Math. MONTPELLIER
|
solv-int nlin.PS nlin.SI patt-sol
| null |
We propose a general algebraic analytic scheme for the spectral transform of
solutions of nonlinear evolution equations. This allows us to give the general
integrable evolution corresponding to an arbitrary time and space dependence of
the spectral transform (in general nonlinear and with non-analytic dispersion
relations). The main theorem is that the compatibility conditions gives always
a true nonlinear evolution because it can always be written as an identity
between polynomials in the spectral variable $k$. This general result is then
used to obtain first a method to generate a new class of solutions to the
nonlinear Schroedinger equation, and second to construct the spectral transform
theory for solving initial-boundary value problems for resonant wave-coupling
processes (like self-induced transparency in two-level media, or stimulated
Brillouin scattering of plasma waves or else stimulated Raman scattering in
nonlinear optics etc...).
|
[
{
"version": "v1",
"created": "Fri, 14 Jan 1994 11:34:18 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Leon",
"Jerome",
""
]
] |
solv-int/9401005
| null |
I.Merola (Phys.Dept.Universita'"La Sapienza", Roma, Italy), O.Ragnisco
(I.N.F.N., Roma, Italy), Tu Gui Zhang (Academia Sinica, People's Rep.China)
|
A Novel Hierarchy of Integrable Lattices
|
Latex file
| null |
10.1088/0266-5611/10/6/009
|
Preprint INFN n.976, Nov.2, 1993
|
solv-int nlin.SI
| null |
In the framework of the reduction technique for Poisson-Nijenhuis structures,
we derive a new hierarchy of integrable lattice, whose continuum limit is the
AKNS hierarchy. In contrast with other differential-difference versions of the
AKNS system, our hierarchy is endowed with a canonical Poisson structure and,
moreover, it admits a vector generalisation. We also solve the associated
spectral problem and explicity contruct action-angle variables through the
r-matrix approach.
|
[
{
"version": "v1",
"created": "Tue, 25 Jan 1994 13:10:31 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Merola",
"I.",
"",
"Phys.Dept.Universita'\"La Sapienza\", Roma, Italy"
],
[
"Ragnisco",
"O.",
"",
"I.N.F.N., Roma, Italy"
],
[
"Zhang",
"Tu Gui",
"",
"Academia Sinica, People's Rep.China"
]
] |
solv-int/9402001
|
Basile Grammaticos
|
B. Grammaticos (LPN, Universit\'e Paris VII, Tour 24-14, Paris,
France), A. Ramani (CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau,
France), K.M. Tamizhmani (Departement of Mathematics, Pondicherry University,
605014 Pondicherry, India)
|
Non Proliferation of Preimages in Integrable Mappings
|
plain tex
| null |
10.1088/0305-4470/27/2/037
| null |
solv-int nlin.SI
| null |
We present an integrability criterion for rational mappings based on two
requirements. First, that a given point should have a unique preimage under the
mapping and, second, that the spontaneously appearing singularities be confined
to a few iteration steps. We present several examples of known integrable
mappings that meet these requirements and, also, use our algorithm in order to
derive new examples of integrable mappings.
|
[
{
"version": "v1",
"created": "Thu, 10 Feb 1994 13:21:09 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Grammaticos",
"B.",
"",
"LPN, Université Paris VII, Tour 24-14, Paris,\n France"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau,\n France"
],
[
"Tamizhmani",
"K. M.",
"",
"Departement of Mathematics, Pondicherry University,\n 605014 Pondicherry, India"
]
] |
solv-int/9402002
| null |
Pol Vanhaecke (Universite de Lille)
|
Integrable systems and symmetric products of curves
|
28 pages, special macros included
| null | null | null |
solv-int nlin.SI
| null |
We show how there is associated to each non-constant polynomial $F(x,y)$ a
completely integrable system with polynomial invariants on $\Rd$ and on
$\C{2d}$ for each $d\geq1$; in fact the invariants are not only in involution
for one Poisson bracket, but for a large class of polynomial Poisson brackets,
indexed by the family of polynomials in two variables. We show that the complex
invariant manifolds are isomorphic to affine parts of $d$-fold symmetric
products of a deformation of the algebraic curve $F(x,y)=0$, and derive the
structure of the real invariant manifolds from it. We also exhibit Lax
equations for the hyperelliptic case (i.e., when $F(x,y)$ is of the form
$y^2+f(x)$) and we show that in this case the invariant manifolds are affine
parts of distinguished (non-linear) subvarieties of the Jacobians of the
curves. As an application the geometry of the H\'enon-Heiles hierarchy --- a
family of superimposable integrable polynomial potentials on the plane --- is
revealed and Lax equations for the hierarchy are given.
|
[
{
"version": "v1",
"created": "Fri, 18 Feb 1994 11:13:36 GMT"
},
{
"version": "v2",
"created": "Tue, 22 Feb 1994 11:16:10 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Vanhaecke",
"Pol",
"",
"Universite de Lille"
]
] |
solv-int/9402003
| null |
Peter Bueken (Katholieke Universiteit Leuven)
|
Multi-Hamiltonian formulation for a class of degenerate completely
integrable systems
|
25 pages, plain TeX, necessary macros included
| null | null | null |
solv-int nlin.SI
| null |
Generalizing a construction of P. Vanhaecke, we introduce a large class of
degenerate (i.e., associated to a degenerate Poisson bracket) completely
integrable systems on (a dense subset of) the space $\R^{2d+n+1}$, called the
generalized master systems. It turns out that certain generalized master
systems (with different Poisson brackets and different Hamiltonians) determine
the same Hamiltonian vector fields (and are therefore different descriptions of
the same Hamiltonian system), and that the Poisson brackets of these systems
are compatible. Consequently, our class of generalized master systems actually
consists of a (smaller) class of completely integrable systems, and our
construction yields a multi-Hamiltonian structure for these systems. As an
application, we construct a multi-Hamiltonian structure for the so-called
master systems introduced by D. Mumford.
|
[
{
"version": "v1",
"created": "Fri, 18 Feb 1994 12:28:56 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Bueken",
"Peter",
"",
"Katholieke Universiteit Leuven"
]
] |
solv-int/9402004
| null |
Didier A Depireux and Jeremy Schiff, U de Montreal and Bar Ilan
|
On UrKdV and UrKP
|
13 pages, plain TeX (no macros), no figures
| null |
10.1007/BF00739799
|
UdeM-LPN-TH-94-191, CRM-2163
|
solv-int hep-th nlin.SI
| null |
We present two extensions of Wilson's explanation of the Miura map from MKdV
to KdV. In the first we explain the map of Svinolupov et al from a certain
UrKdV-like equation to KdV, and in the second we explain Konopelchenko's map
from the modified KP equation to KP. In the course of the latter we introduce
an ``UrKP'' system, with an infinite dimensional symmetry, providing us with a
systematic method to construct Backlund transformations for the modified KP and
KP equations.
|
[
{
"version": "v1",
"created": "Tue, 1 Mar 1994 21:15:44 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Depireux",
"Didier A",
""
],
[
"Schiff",
"Jeremy",
""
],
[
"de Montreal",
"U",
""
],
[
"Ilan",
"Bar",
""
]
] |
solv-int/9403001
|
Ron Perline
|
Joel Langer (Case Western Reserve), Ron Perline (Drexel University)
|
The planar filament equation
|
13 pages, AMSTeX, includes four figures (use associated PS file). To
appear in Mechanics Day Proceedings, Fields Institute, June 1992
| null | null | null |
solv-int nlin.SI
| null |
The planar filament equation and its relation to the modified
Korteweg-deVries equation are studied in the context of Poisson geometry. The
structure of the planar filament equation is shown to be similar to that of the
3-D localized induction equation, previously studied by the authors.
|
[
{
"version": "v1",
"created": "Fri, 25 Mar 1994 18:42:28 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Langer",
"Joel",
"",
"Case Western Reserve"
],
[
"Perline",
"Ron",
"",
"Drexel University"
]
] |
solv-int/9404001
|
Ron Perline
|
Joel Langer (Case Western Reserve University), Ron Perline (Drexel
University)
|
Localized induction equation, Heisenberg chain, and nonlinear
Schrodinger equation
|
9 pages, AMSTeX. To appear in Mechanics Day Proceedings, Fields
Institute, June 1992
| null | null |
Drexel MCS Report 4.1.1
|
solv-int nlin.SI
| null |
The three equations named in the title are examples of infinite-dimensional
completely integrable Hamiltonian systems, and are related to each other via
simple geometric constructions. In this paper, these interrelationships are
further explained in terms of the recursion operator for the Localized
Induction Equation, and the recursion operator is seen to play a variety of
roles in key geometric variational formulas.
|
[
{
"version": "v1",
"created": "Mon, 4 Apr 1994 17:57:59 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Langer",
"Joel",
"",
"Case Western Reserve University"
],
[
"Perline",
"Ron",
"",
"Drexel\n University"
]
] |
solv-int/9404002
|
R. A. Sharipov
|
R. A. Sharipov (Department of Mathematics, Bashkir State University,
Ufa, Russia)
|
Dynamical Systems Accepting the Normal Shift
|
2 pages, AMS-TeX, version 2.1, size 6 Kbytes (ASCII). Report on 16-th
joint session of Seminar of I.G. Petrovsky and Moscow Mathematical Society at
Moscow State University. January 19, 1994. To be published in: Uspehi Mat.
Nauk
| null | null | null |
solv-int alg-geom astro-ph gr-qc hep-th math.AG nlin.SI
| null |
Newtonian dynamical systems accepting the normal shift on an arbitrary
Riemannian manifold are considered. Partial differential equations forming the
weak and additional normality conditions for them are reported.
|
[
{
"version": "v1",
"created": "Wed, 7 Apr 1993 05:14:24 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Sharipov",
"R. A.",
"",
"Department of Mathematics, Bashkir State University,\n Ufa, Russia"
]
] |
solv-int/9404003
|
R. A. Sharipov
|
R. A. Sharipov (home address: Rabochaya str. 5, Ufa 450003, Russia)
|
Problem of Metrizability for the Dynamical Systems Accepting the Normal
Shift
|
8 pages (26 Kbytes), AmS-TeX, version 2.1. To be published in Theor.
and Math. Phys. (Russian)
| null |
10.1007/BF01079259
| null |
solv-int nlin.SI
| null |
The problem of metrizability for the dynamical systems accepting the normal
shift is formulated and solved. The explicit formula for the force field of
metrizable Newtonian dynamical system $\ddot\bold r=\bold F(\bold r,\dot\bold
r)$ is found.
|
[
{
"version": "v1",
"created": "Sun, 18 Apr 1993 03:22:32 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Sharipov",
"R. A.",
"",
"home address: Rabochaya str. 5, Ufa 450003, Russia"
]
] |
solv-int/9404004
|
Evgeny Doktorov
|
Evgeny V.Doktorov and Rafael A.Vlasov (Institute of Physics, 220072
Minsk, Belarus)
|
Spatial Solitons in Media with Delayed-Response Optical Nonlinearities
|
7 pages, to be published in Europhys. Lett
| null |
10.1209/0295-5075/26/7/002
| null |
solv-int nlin.PS nlin.SI patt-sol
| null |
Near-soliton scanning light-beam propagation in media with both
delayed-response Kerr-type and thermal nonlinearities is analyzed. The
delayed-response part of the Kerr nonlinearity is shown to be competitive as
compared to the thermal nonlinearity, and relevant contributions to a
distortion of the soliton form and phase can be mutually compensated. This
quasi-soliton beam propagation regime keeps properties of the incli- ned
self-trapped channel.
|
[
{
"version": "v1",
"created": "Wed, 20 Apr 1994 18:15:34 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Doktorov",
"Evgeny V.",
"",
"Institute of Physics, 220072\n Minsk, Belarus"
],
[
"Vlasov",
"Rafael A.",
"",
"Institute of Physics, 220072\n Minsk, Belarus"
]
] |
solv-int/9404005
|
Evgeny Doktorov
|
Evgeny V.Doktorov (Institute of Physics, 220072 Minsk, Belarus)
|
Non-Linear Evolution Equations with Non-Analytic Dispersion Relations in
2+1 Dimensions. Bilocal Approach
|
13 pages, to be published in J. Phys. A
| null |
10.1088/0305-4470/27/10/024
| null |
solv-int nlin.PS nlin.SI patt-sol
| null |
A method is proposed of obtaining (2+1)-dimensional non- linear equations
with non-analytic dispersion relations. Bilocal formalism is shown to make it
possible to represent these equations in a form close to that for their
counterparts in 1+1 dimensions.
|
[
{
"version": "v1",
"created": "Wed, 20 Apr 1994 18:14:18 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Doktorov",
"Evgeny V.",
"",
"Institute of Physics, 220072 Minsk, Belarus"
]
] |
solv-int/9404006
|
Jarmo Hietarinta
|
B. Grammaticos (LPN, Universite Paris VII, Tour 24-14, 5eme etage,
75251 Paris, France), A. Ramani and J. Hietarinta (CPT, Ecole Polytechnique,
91128 Palaiseau, France)
|
Multilinear Operators: The Natural Extension Of Hirota's Bilinear
Formalism
|
9 pages in plain TeX
| null |
10.1016/0375-9601(94)90367-0
| null |
solv-int nlin.SI
| null |
We introduce multilinear operators, that generalize Hirota's bilinear $D$
operator, based on the principle of gauge invariance of the $\tau$ functions.
We show that these operators can be constructed systematically using the
bilinear $D$'s as building blocks. We concentrate in particular on the
trilinear case and study the possible integrability of equations with one
dependent variable. The 5th order equation of the Lax-hierarchy as well as
Satsuma's lowest-order gauge invariant equation are shown to have simple
trilinear expressions. The formalism can be extended to an arbitrary degree of
multilinearity.
|
[
{
"version": "v1",
"created": "Tue, 26 Apr 1994 11:38:01 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Grammaticos",
"B.",
"",
"LPN, Universite Paris VII, Tour 24-14, 5eme etage,\n 75251 Paris, France"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique,\n 91128 Palaiseau, France"
],
[
"Hietarinta",
"J.",
"",
"CPT, Ecole Polytechnique,\n 91128 Palaiseau, France"
]
] |
solv-int/9406001
|
Ron Perline
|
Ron Perline (Department of Mathematics and Computer Science, Drexel
University)
|
Localized induction equation and pseudospherical surfaces
|
21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and General
| null |
10.1088/0305-4470/27/15/029
| null |
solv-int hep-th nlin.SI
| null |
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.
|
[
{
"version": "v1",
"created": "Sat, 11 Jun 1994 16:47:27 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Perline",
"Ron",
"",
"Department of Mathematics and Computer Science, Drexel\n University"
]
] |
solv-int/9406002
|
Freddy Christiansen
|
Freddy Christiansen (INO, Largo E. Fermi 6, Firenze, Italy), Hans
Henrik Rugh (IHES, 35 Route de Chartres, Bures-sur Yvette, France) and Svend
Erik Rugh (NBI, Blegdamsvej 17, Copenhagen, Denmark)
|
Non-integrability of the mixmaster universe
|
11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures
compressed and uuencoded with uufiles. Revised version to appear in J Phys. A
|
J.Phys. A28 (1995) 657-668
|
10.1088/0305-4470/28/3/019
| null |
solv-int chao-dyn gr-qc nlin.CD nlin.SI
| null |
We comment on an analysis by Contopoulos et al. which demonstrates that the
governing six-dimensional Einstein equations for the mixmaster space-time
metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case
irrespective of the value, $I$, of the generating Hamiltonian which is a
constant of motion. For $I < 0$ we find numerous closed orbits with two
unstable eigenvalues strongly indicating that there cannot exist two additional
first integrals apart from the Hamiltonian and thus that the system, at least
for this case, is very likely not integrable. In addition, we present numerical
evidence that the average Lyapunov exponent nevertheless vanishes. The model is
thus a very interesting example of a Hamiltonian dynamical system, which is
likely non-integrable yet passes the reduced Painlev\'{e} test.
|
[
{
"version": "v1",
"created": "Mon, 13 Jun 1994 15:46:10 GMT"
},
{
"version": "v2",
"created": "Sun, 18 Dec 1994 15:35:27 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Christiansen",
"Freddy",
"",
"INO, Largo E. Fermi 6, Firenze, Italy"
],
[
"Rugh",
"Hans Henrik",
"",
"IHES, 35 Route de Chartres, Bures-sur Yvette, France"
],
[
"Rugh",
"Svend Erik",
"",
"NBI, Blegdamsvej 17, Copenhagen, Denmark"
]
] |
solv-int/9407001
|
Asher Yahalom
|
Asher Yahalom
|
Helicity Conservation via the Noether Theorem
|
7 pages of tex
| null |
10.1063/1.531123
| null |
solv-int nlin.SI
| null |
The conservation of helicity in ideal barotropic fluids is discussed from a
group theoretical point of view. A new symmetry group is introduced i.e. the
alpha group of translations. It is proven via the Noether theorem that this
group generates helicity conservation.
|
[
{
"version": "v1",
"created": "Fri, 1 Jul 1994 11:38:19 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Yahalom",
"Asher",
""
]
] |
solv-int/9407002
|
Ralph Willox
|
Ralph Willox (1), Willy Hereman (2) and Frank Verheest (3) ((1) Dienst
Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B--1050
Brussel, Belgium (2) Department of Mathematical and Computer Sciences,
Colorado School of Mines, Golden, Colorado 80401--1887, USA (3) Sterrenkundig
Observatorium, Universiteit Gent, Krijgslaan 281, B--9000 Gent, Belgium)
|
Complete integrability of a modified vector derivative nonlinear
Schroedinger equation
|
LateX (17 pages)
| null |
10.1088/0031-8949/52/1/003
| null |
solv-int nlin.SI
| null |
Oblique propagation of magnetohydrodynamic waves in warm plasmas is described
by a modified vector derivative nonlinear Schroedinger equation, if charge
separation in Poisson's equation and the displacement current in Ampere's law
are properly taken into account. This modified equation cannot be reduced to
the standard derivative nonlinear Schroedinger equation and hence its possible
integrability and related properties need to be established afresh. Indeed, the
new equation is shown to be integrable by the existence of a bi--Hamiltonian
structure, which yields the recursion operator needed to generate an infinite
sequence of conserved densities. Some of these have been found explicitly by
symbolic computations based on the symmetry properties of the new equation.
Since the new equation includes as a special case the derivative nonlinear
Schroedinger equation, the recursion operator for the latter one is now readily
available.
|
[
{
"version": "v1",
"created": "Thu, 14 Jul 1994 10:22:59 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Willox",
"Ralph",
""
],
[
"Hereman",
"Willy",
""
],
[
"Verheest",
"Frank",
""
]
] |
solv-int/9407003
|
R. A. Sharipov
|
M.V. Pavlov (Landau Institute for Theor. Physics., Moscow, Russia),
R.A. Sharipov (Dep. of Math., Bashkir State Univ., Ufa, Russia) and S.I.
Svinolupov (Inst. of Math., Ufa, Russia)
|
Invariant Integrability Criterion for the Equations of Hydrodynamical
Type
| null | null | null |
solv-int nlin.SI
| null |
Invariant integrability criterion for the equations of hydrodynamical type is
found. This criterion is written in the form of vanishing for some tensor which
is derived from the velocities matrix of hydrodynamical equations.
|
[
{
"version": "v1",
"created": "Sun, 18 Jul 1993 02:37:03 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Pavlov",
"M. V.",
"",
"Landau Institute for Theor. Physics., Moscow, Russia"
],
[
"Sharipov",
"R. A.",
"",
"Dep. of Math., Bashkir State Univ., Ufa, Russia"
],
[
"Svinolupov",
"S. I.",
"",
"Inst. of Math., Ufa, Russia"
]
] |
|
solv-int/9407004
|
Vsevolod Adler
|
V.E. Adler
|
Integrable deformations of a polygon
|
8 pp, LaTeX, 18K
| null |
10.1016/0167-2789(95)00124-M
| null |
solv-int nlin.SI
| null |
The new integrable mapping with a simple geometric interpretation is
presented. This mapping arise from the nonlinear superposition principle for
the B\"acklund transformations of some vector evolution equation.
|
[
{
"version": "v1",
"created": "Tue, 19 Jul 1994 07:49:09 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Adler",
"V. E.",
""
]
] |
solv-int/9407005
|
Adam Doliwa
|
Adam Doliwa (Institute of Theoretical Physics, Warsaw University),
Paolo Maria Santini (Dipartimento di Fisica, Universita di Roma "La Sapienza"
and INFN Sezione di Roma)
|
Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy
|
LaTeX file, 14 pages + 4 figures
|
J. Math. Phys. 36 (1995) 1259
|
10.1063/1.531119
|
IFT/6/94
|
solv-int nlin.SI
| null |
We show that the following elementary geometric properties of the motion of a
discrete (i.e. piecewise linear) curve select the integrable dynamics of the
Ablowitz-Ladik hierarchy of evolution equations: i) the set of points
describing the discrete curve lie on the sphere S^3, ii) the distance between
any two subsequant points does not vary in time, iii) the dynamics does not
depend explicitly on the radius of the sphere. These results generalize to a
discrete context our previous work on continuous curves.
|
[
{
"version": "v1",
"created": "Wed, 27 Jul 1994 19:34:43 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
],
[
"Santini",
"Paolo Maria",
"",
"Dipartimento di Fisica, Universita di Roma \"La Sapienza\"\n and INFN Sezione di Roma"
]
] |
solv-int/9408001
|
Hua Wu
|
Hua Wu and D. W. L. Sprung (Department of Physics and Astronomy,
McMaster University Hamilton, Ontario, Canada), J. Martorell (Dept.
d'Estructura i Constituents de la Materia, Facultat Fisica, University of
Barcelona, Spain)
|
Numerical investigation of iso-spectral cavities built from triangles
|
15 pages, revtex, 5 postscript figures
| null |
10.1103/PhysRevE.51.703
| null |
solv-int nlin.SI
| null |
We present computational approaches as alternatives to the recent microwave
cavity experiment by S. Sridhar and A. Kudrolli (Phys. Rev. Lett. {\bf 72},
2175 (1994)) on iso-spectral cavities built from triangles. A straightforward
proof of iso-spectrality is given based on the mode matching method. Our
results show that the experiment is accurate to 0.3% for the first 25 states.
The level statistics resemble those of GOE when the integrable part of the
spectrum is removed.
|
[
{
"version": "v1",
"created": "Wed, 17 Aug 1994 15:09:20 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Wu",
"Hua",
"",
"Department of Physics and Astronomy,\n McMaster University Hamilton, Ontario, Canada"
],
[
"Sprung",
"D. W. L.",
"",
"Department of Physics and Astronomy,\n McMaster University Hamilton, Ontario, Canada"
],
[
"Martorell",
"J.",
"",
"Dept.\n d'Estructura i Constituents de la Materia, Facultat Fisica, University of\n Barcelona, Spain"
]
] |
solv-int/9409001
|
Frank Nijhoff
|
H.W. Capel and F.W. Nijhoff
|
Integrable Quantum Mappings
|
13 pages, to appear in Proceedings of the Intl. Workshop on
Symmetries and Integrability of Difference Equations, eds. D. Levi, L. Vinet
and P. Winternitz
| null | null | null |
solv-int nlin.SI
| null |
We discuss the canonical structure of a class of integrable quantum mappings,
i.e. iterative canonical transformations that can be interpreted as a discrete
dynamical system. As particular examples we consider quantum mappings
associated with the lattice analogues of the KdV and MKdV equations. These
mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the
existence of commuting families of exact quantum invariants. We derive the
associated quantum Miura transformations between these mappings and the
corresponding quantum bi-Hamiltonian structure.
|
[
{
"version": "v1",
"created": "Fri, 2 Sep 1994 12:33:10 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Capel",
"H. W.",
""
],
[
"Nijhoff",
"F. W.",
""
]
] |
solv-int/9409002
|
Dr "P. A" Clarkson
|
Andrew P. Bassom and Peter A. Clarkson (Department of Mathematics,
University of Exeter, Exeter, U.K.)
|
New exact solutions for the discrete fourth Painlev\'e equation
|
Tex file 14 pages
| null |
10.1016/0375-9601(94)91294-7
|
M27/94 (to be published in Physics Letters A)
|
solv-int nlin.SI
| null |
In this paper we derive a number of exact solutions of the discrete equation
$$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})=
{-2z_nx_n^3+(\eta-3\delta^{-2}-z_n^2)x_n^2+\mu^2\over
(x_n+z_n+\gamma)(x_n+z_n-\gamma)},\eqno(1)$$ where $z_n=n\delta$ and $\eta$,
$\delta$, $\mu$ and $\gamma$ are constants. In an appropriate limit (1) reduces
to the fourth \p\ (PIV) equation $${\d^2w\over\d z^2} = {1\over2w}\left({\d
w\over\d z}\right)^2+\tfr32w^3 + 4zw^2 + 2(z^2-\alpha)w +{\beta\over
w},\eqno(2)$$ where $\alpha$ and $\beta$ are constants and (1) is commonly
referred to as the discretised fourth Painlev\'e equation. A suitable
factorisation of (1) facilitates the identification of a number of solutions
which take the form of ratios of two polynomials in the variable $z_n$. Limits
of these solutions yield rational solutions of PIV (2). It is also known that
there exist exact solutions of PIV (2) that are expressible in terms of the
complementary error function and in this article we show that a discrete
analogue of this function can be obtained by analysis of (1).
|
[
{
"version": "v1",
"created": "Fri, 16 Sep 1994 15:32:03 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Bassom",
"Andrew P.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
],
[
"Clarkson",
"Peter A.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
]
] |
solv-int/9409003
|
Dr "P. A" Clarkson
|
Peter A. Clarkson and Elizabeth L. Mansfield (Department of
Mathematics, University of Exeter, Exeter, U.K.)
|
Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations
|
Tex file 19 pages, figures available from author
| null | null |
M94/36, Department of Mathematics, University of Exeter
|
solv-int nlin.SI
| null |
In this paper we study symmetry reductions and exact solutions of the shallow
water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} -
u_{xt} - u_{xx} = 0,\eqno(1)$$ where $\alpha$ and $\beta$ are arbitrary,
nonzero, constants, which is derivable using the so-called Boussinesq
approximation. Two special cases of this equation, or the equivalent nonlocal
equation obtained by setting $u_x=U$, have been discussed in the literature.
The case $\alpha=2\beta$ was discussed by Ablowitz, Kaup, Newell and Segur
[{\it Stud.\ Appl.\ Math.}, {\bf53} (1974) 249], who showed that this case was
solvable by inverse scattering through a second order linear problem. This case
and the case $\alpha=\beta$ were studied by Hirota and Satsuma [{\it J.\ Phys.\
Soc.\ Japan}, {\bf40} (1976) 611] using Hirota's bi-linear technique. Further
the case $\alpha=\beta$ is solvable by inverse scattering through a third order
linear problem. In this paper a catalogue of symmetry reductions is obtained
using the classical Lie method and the nonclassical method due to Bluman and
Cole [{\it J.\ Math.\ Mech.\/}, {\bf 18} (1969) 1025]. The classical Lie method
yields symmetry reductions of (1) expressible in terms of the first, third and
fifth \p\ transcendents and Weierstrass elliptic functions. The nonclassical
method yields a plethora of exact solutions of (1) with $\alpha=\beta$ which
possess a rich variety of qualitative behaviours. These solutions all like a
two-soliton solution for $t<0$ but differ radically for $t>0$ and may be viewed
as a nonlinear superposition of two solitons, one travelling to the left with
arbitrary speed and the other to the right with equal and opposite speed.
|
[
{
"version": "v1",
"created": "Fri, 23 Sep 1994 13:14:21 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Clarkson",
"Peter A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Mansfield",
"Elizabeth L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
]
] |
solv-int/9409004
|
Yavuz Nutku
|
E. V. Ferapontov and Y. Nutku
|
On the Monge-Ampere equivalent of the sine-Gordon equation
|
latex
| null |
10.1088/0305-4470/27/23/026
| null |
solv-int nlin.SI
| null |
Surfaces of constant negative curvature in Euclidean space can be described
by either the sine-Gordon equation for the angle between asymptotic directions,
or a Monge-Ampere equation for the graph of the surface. We present the
explicit form of the correspondence between these two integrable non-linear
partial differential equations using their well-known properties in
differential geometry. We find that the cotangent of the angle between
asymptotic directions is directly related to the mean curvature of the surface.
This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere
equations.
|
[
{
"version": "v1",
"created": "Mon, 3 Oct 1994 08:55:56 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Ferapontov",
"E. V.",
""
],
[
"Nutku",
"Y.",
""
]
] |
solv-int/9410001
|
Nimmo Jjc
|
J J C NIMMO(Department of Mathematics, University of Glasgow, Glasgow
G12 8QW, Scotland)
|
Darboux Transformations from Reductions of the KP Hierarchy
|
10 pages, LaTeX2e plus Latex2e style file for layout. (Should work
with LaTeX209 with minimum changes (see line 3 of source))
| null | null |
University of Glasgow, Department of Mathematics, Paper No. 94/54
|
solv-int nlin.SI
| null |
The use of effective Darboux transformations for general classes Lax pairs is
discussed. The general construction of ``binary'' Darboux transformations
preserving certain properties of the operator, such as self-adjointness, is
given. The classes of Darboux transformations found include the multicomponent
BKP and CKP reductions of the KP hierarchy.
|
[
{
"version": "v1",
"created": "Tue, 11 Oct 1994 16:10:47 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"NIMMO",
"J J C",
"",
"Department of Mathematics, University of Glasgow, Glasgow\n G12 8QW, Scotland"
]
] |
solv-int/9410002
|
Troy Shinbrot
|
Troy Shinbrot (Northwestern University), J.M. Ottino (Northwestern
University)
|
Maps, PDE's and Solitary Waves
|
28 pages, Binhexed Macintosh MS Word 5.1 file follows; available in
hardcopy by request ([email protected]). In press: Int. J. Bif. &
Chaos
| null |
10.1142/S0218127495000429
| null |
solv-int chao-dyn nlin.CD nlin.PS nlin.SI patt-sol
| null |
We describe a map-based model which reproduces many of the behaviors seen in
partial differential equations (PDE's). Like PDE's, we show that this model can
support an infinite number of stationary solutions, traveling solutions,
breathing solutions, and elastically colliding solutions. Unlike PDE's, the
model can be applied with minimal computational machinery, and few sources of
numerical error. Moreover, this model clarifies possible mechanisms by which
various coherent solutions are maintained in the face of dispersion.
|
[
{
"version": "v1",
"created": "Thu, 13 Oct 1994 21:58:42 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Shinbrot",
"Troy",
"",
"Northwestern University"
],
[
"Ottino",
"J. M.",
"",
"Northwestern\n University"
]
] |
solv-int/9410003
|
Grinevich Piotr
|
Piotr G.Grinevich and Roman G.Novikov
|
Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy
Dispersion Relations for the Fast Decaying Potentials
|
38 pages, TeX
| null |
10.1007/BF02099609
| null |
solv-int funct-an hep-th math.FA nlin.SI
| null |
For the two-dimensional Schr\"odinger equation $$ [- \Delta
+v(x)]\psi=E\psi,\ x\in \R^2,\ E=E_{fixed}>0 \ \ \ \ \ (*)$$ at a fixed
positive energy with a fast decaying at infinity potential $v(x)$ dispersion
relations on the scattering data are given.Under "small norm" assumption using
these dispersion relations we give (without a complete proof of sufficiency) a
characterization of scattering data for the potentials from the Schwartz class
$S=C_{\infty}^{(\infty)} (\hbox{\bf R}^2).$ For the potentials with zero
scattering amplitude at a fixed energy $\scriptstyle E_{fixed}$ (transparent
potentials) we give a complete proof of this characterization. As a consequence
we construct a family (parameterized by a function of one variable) of
two-dimensional spherically-symmetric real potentials from the Schwartz class
$S$ transparent at a given energy. For the two-dimensional case (without
assumption that the potential is small) we show that there are no nonzero real
exponentially decreasing at infinity, potentials transparent at a fixed energy.
For any dimension greater or equal 1 we prove that there are no nonzero real
potentials with zero forward scattering amplitude at an energy interval. We
show that KdV-type equations in dimension 2+1 related with the scattering
problem $(*)$ (the Novikov-Veselov equations) do not preserve, in general,
these dispersion relations starting from the second one. As a corollary these
equations do not preserve, in general , the decay rate faster then $|x|^{-3}$
for initial data from the Schwartz class.
|
[
{
"version": "v1",
"created": "Wed, 26 Oct 1994 10:53:46 GMT"
},
{
"version": "v2",
"created": "Fri, 28 Oct 1994 18:04:49 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Grinevich",
"Piotr G.",
""
],
[
"Novikov",
"Roman G.",
""
]
] |
solv-int/9410004
| null |
Steven Nerney ( National Research Council Associate, NASA-Marshall
Space Flight Center, Alabama 35812), Edward J. Schmahl (Astronomy Department,
University of Maryland, College Park, MD 20742) and Z. E. Musielak
(Department of Mechanical and Aerospace Engineering, and Center for Space
Plasmas and Aeronomic Research, University of Alabama at Huntsville,
Huntsville, Alabama 35899)
|
Analytic Solutions of the Vector Burgers' Equation
|
one postscript figure (22K) appended to paper
| null | null |
93-120
|
solv-int nlin.SI
| null |
The well-known analytical solution of Burgers' equation is extended to
curvilinear coordinate systems in three-dimensions by a method which is much
simpler and more suitable to practical applications than that previously used.
The results obtained are applied to incompressible flow with cylindrical
symmetry, and also to the decay of an initially linearly increasing wind.
|
[
{
"version": "v1",
"created": "Tue, 1 Nov 1994 16:05:51 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Nerney",
"Steven",
"",
"National Research Council Associate, NASA-Marshall\n Space Flight Center, Alabama 35812"
],
[
"Schmahl",
"Edward J.",
"",
"Astronomy Department,\n University of Maryland, College Park, MD 20742"
],
[
"Musielak",
"Z. E.",
"",
"Department of Mechanical and Aerospace Engineering, and Center for Space\n Plasmas and Aeronomic Research, University of Alabama at Huntsville,\n Huntsville, Alabama 35899"
]
] |
solv-int/9411001
|
Metin Gurses
|
Burak Gurel, Metin Gurses and Ismagil Habibullin
|
Boundary Value Problems For Integrable Equations Compatible With The
Symmetry Algebra
|
25 pages , Latex , no figures
| null |
10.1063/1.531189
| null |
solv-int nlin.SI
| null |
Boundary value problems for integrable nonlinear partial differential
equations are considered from the symmetry point of view. Families of boundary
conditions compatible with the Harry-Dym, KdV and MKdV equations and the
Volterra chain are discussed. We also discuss the uniqueness of some of these
boundary conditions.
|
[
{
"version": "v1",
"created": "Wed, 9 Nov 1994 10:40:03 GMT"
},
{
"version": "v2",
"created": "Thu, 10 Nov 1994 07:36:56 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Gurel",
"Burak",
""
],
[
"Gurses",
"Metin",
""
],
[
"Habibullin",
"Ismagil",
""
]
] |
solv-int/9411002
|
Sergej Flach
|
S. Flach
|
On the Existence of Localized Excitations in Nonlinear Hamiltonian
Lattices
|
13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press)
| null |
10.1103/PhysRevE.51.1503
| null |
solv-int nlin.SI
| null |
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.
|
[
{
"version": "v1",
"created": "Mon, 14 Nov 1994 23:25:24 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Flach",
"S.",
""
]
] |
solv-int/9411003
|
Jarmo Hietarinta
|
J. Hietarinta (Department of Physics, University of Turku, 20500
Turku, Finland), B. Grammaticos (LPN, Universite Paris VII, Tour 24-14, 5eme
etage, 75251 Paris, France) and A. Ramani (CPT, Ecole Polytechnique, 91128
Palaiseau, France)
|
Integrable Trilinear PDE's
|
10 pages in plain TeX
| null | null | null |
solv-int nlin.SI
| null |
In a recent publication we proposed an extension of Hirota's bilinear
formalism to arbitrary multilinearities. The trilinear (and higher) operators
were constructed from the requirement of gauge invariance for the nonlinear
equation. Here we concentrate on the trilinear case, and use singularity
analysis in order to single out equations that are likely to be integrable. New
PDE's are thus obtained, along with others already well-known for their
integrability and for which we obtain here the trilinear expression. To appear
in the proceedings of NEEDS'94 (11-18 September, Los Alamos)
|
[
{
"version": "v1",
"created": "Wed, 16 Nov 1994 15:06:05 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Hietarinta",
"J.",
"",
"Department of Physics, University of Turku, 20500\n Turku, Finland"
],
[
"Grammaticos",
"B.",
"",
"LPN, Universite Paris VII, Tour 24-14, 5eme\n etage, 75251 Paris, France"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique, 91128\n Palaiseau, France"
]
] |
solv-int/9411004
|
Metin Gurses
|
Metin Gurses and Atalay Karasu
|
Variable Coefficient Third Order KdV Type of Equations
|
Latex file , 15 pages
| null |
10.1063/1.530974
| null |
solv-int nlin.SI
| null |
We show that the integrable subclassess of a class of third order
non-autonomous equations are identical with the integrable subclassess of the
autonomous ones.
|
[
{
"version": "v1",
"created": "Wed, 16 Nov 1994 14:28:19 GMT"
},
{
"version": "v2",
"created": "Thu, 17 Nov 1994 08:52:42 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Gurses",
"Metin",
""
],
[
"Karasu",
"Atalay",
""
]
] |
solv-int/9411005
| null |
Steven Nerney (National Research Council Associate, NASA-Marshall
Space Flight Center, Alabama 35812), Edward J. Schmahl (Astronomy Department,
University of Maryland, College Park, MD 20742) and Z. E. Musielak
(Department of Mechanical and Aerospace Engineering, and Center for Space
Plasmas and Aeronomic Research, University of Alabama at Huntsville,
Huntsville, Alabama 35899)
|
Limits to Extensions of Burgers Equation
|
Plain Tex, no figures
| null | null |
94-107
|
solv-int astro-ph chao-dyn comp-gas nlin.CD nlin.CG nlin.SI
| null |
The vector Burgers equation is extended to include pressure gradients and
gravity. It is shown that within the framework of the Cole-Hopf transformation
there are no physical solutions to this problem. This result is important
because it clearly demonstrates that any extension of Burgers equation to more
interesting physical situations is strongly limited.
|
[
{
"version": "v1",
"created": "Thu, 17 Nov 1994 22:33:09 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Nerney",
"Steven",
"",
"National Research Council Associate, NASA-Marshall\n Space Flight Center, Alabama 35812"
],
[
"Schmahl",
"Edward J.",
"",
"Astronomy Department,\n University of Maryland, College Park, MD 20742"
],
[
"Musielak",
"Z. E.",
"",
"Department of Mechanical and Aerospace Engineering, and Center for Space\n Plasmas and Aeronomic Research, University of Alabama at Huntsville,\n Huntsville, Alabama 35899"
]
] |
solv-int/9411006
|
Kenji Kajiwara
|
Y.Ohta(Dept. Appl. Math., Hiroshima Univ.), K.Kajiwara(Dept. Elecrical
Eng., Doshisha Univ.), and J.Satsuma(Dept. Math. Sci., Univ. Tokyo)
|
Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I
Equation
|
6 pages in LaTeX, to appear in Proceedings of the Workshop on
Symmetries and Integrability of Difference Equations, CRM Proceedings and
Lecture Notes Series, AMS, 1994
| null | null | null |
solv-int hep-th nlin.SI
| null |
Bilinear structure for the discrete Painlev\'e I equation is investigated.
The solution on semi-infinite lattice is given in terms of the Casorati
determinant of discrete Airy function. Based on this fact, the discrete
Painlev\'e I equation is naturally extended to a discrete coupled system.
Corresponding matrix model is also mentioned.
|
[
{
"version": "v1",
"created": "Wed, 30 Nov 1994 06:09:34 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Ohta",
"Y.",
"",
"Dept. Appl. Math., Hiroshima Univ."
],
[
"Kajiwara",
"K.",
"",
"Dept. Elecrical\n Eng., Doshisha Univ."
],
[
"Satsuma",
"J.",
"",
"Dept. Math. Sci., Univ. Tokyo"
]
] |
solv-int/9412001
|
R. A. Sharipov
|
R.A. Sharipov (Dep. of Math., Bashkir State University, Ufa, Russia),
R.I. Yamilov (Inst. of Math. UrO RAN, Chernishevsky 112, Ufa, Russia)
|
B\"acklund transformation and the construction of the integrable
boundary-value problem for the equation $u_{xx}-u_{tt}=e^u-e^{-2u}$
|
7 pages AmS-TeX, Published in book: Problems of Math. Physics and the
asymptotics of their solutions, (V.Yu. Novokshenov, ed.) Inst. of Math. UrO
AN SSSR, Ufa, 1991, pp. 66-77
| null | null | null |
solv-int nlin.SI
| null |
B\"acklund transformation for the Bullough-Dodd-Jiber-Shabat equation
$u_{xx}-u_{tt}=e^u-e^{-2u}$ is found. The construction of integrable boundary
condition for this equation together with the algebro-geometric solutions
satisfying it are suggested.
|
[
{
"version": "v1",
"created": "Mon, 5 Dec 1994 05:33:27 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Sharipov",
"R. A.",
"",
"Dep. of Math., Bashkir State University, Ufa, Russia"
],
[
"Yamilov",
"R. I.",
"",
"Inst. of Math. UrO RAN, Chernishevsky 112, Ufa, Russia"
]
] |
solv-int/9412002
|
Dr "P. A" Clarkson
|
Peter A. Clarkson and Andrew P. Bassom (Department of Mathematics,
University of Exeter, Exeter, U.K.)
|
Backlund Transformations and Hierarchies of Exact Solutions for the
Fourth Painleve Equation and their Application to Discrete Equations
|
Tex file 13 pages
| null | null |
M94/42, Department of Mathematics, University of Exeter
|
solv-int nlin.SI
| null |
In this paper we describe B\"acklund transformations and hierarchies of exact
solutions for the fourth Painlev\'e equation (PIV) $${\d^2 w\over\d
z^2}={1\over2w}\left(\d w\over\d z\right)^2 + {{3\over2}}w^3 + 4zw^2 +
2(z^2-\alpha)w+{\beta\over w},\eqno(1){\hbox to 16pt{\hfill}}$$ with $\alpha$,
$\beta$ constants. Specifically, a nonlinear superposition principle for PIV,
hierarchies of solutions expressible in terms of complementary error or
parabolic cylinder functions as well as rational solutions will be derived.
Included amongst these hierarchies are solutions of (1) for which
$\alpha=\pm\tfr12n$ and $\beta=-\tfr12n^2$, with $n$ an integer. These
particular forms arise in quantum gravity and also satisfy a discrete analogue
of the first Painlev\'e equation. We also obtain a number of exact solutions of
the discrete fourth Painlev\'e equation $$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})=
{-2z_nx_n^3+(\eta-3\delta^{-2}-z_n^2)x_n^2+\mu^2\over
(x_n+z_n+\gamma)(x_n+z_n-\gamma)},\eqno(2){\hbox to 16pt{\hfill}}$$}%
{\narrower\noindent\baselineskip=12pt where $z_n=n\delta$ and $\eta$, $\delta$,
$\mu$ and $\gamma$ are constants, which, in an appropriate limit, reduces to
PIV (1). A suitable factorisation of (2) facilitates the identification of a
number of solutions which take the form of ratios of two polynomials in the
variable $z_n$ and the limits of these solutions yield rational solutions of
(1).
|
[
{
"version": "v1",
"created": "Fri, 9 Dec 1994 11:48:03 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Clarkson",
"Peter A.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
],
[
"Bassom",
"Andrew P.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
]
] |
solv-int/9412003
|
Dr "P. A" Clarkson
|
P.A. Clarkson, E.L. Mansfield and A.E. Milne (Department of
Mathematics, University of Exeter, Exeter, U.K.)
|
Symmetries and Exact Solutions of a 2+1-dimensional Sine-Gordon System
|
Tex file 22 pages, figures available from author
| null | null |
M94/44, Department of Mathematics, University of Exeter
|
solv-int nlin.SI
| null |
We investigate the classical and nonclassical reductions of the
$2+1$-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a
strong generalisation of the sine-Gordon equation. A family of solutions
obtained as a nonclassical reduction involves a decoupled sum of solutions of a
generalised, real, pumped Maxwell-Bloch system. This implies the existence of
families of solutions, all occurring as a decoupled sum, expressible in terms
of the second, third and fifth Painlev\'e transcendents, and the sine-Gordon
equation. Indeed, hierarchies of such solutions are found, and explicit
transformations connecting members of each hierarchy are given. By applying a
known B\"acklund transformation for the system to the new solutions found, we
obtain further families of exact solutions, including some which are expressed
as the argument and modulus of sums of products of Bessel functions with
arbitrary coefficients. Finally, we prove the sine-Gordon system has the
Painlev\'e property, which requires the usual test to be modified, and derive a
non-isospectral Lax pair for the generalised, real, pumped Maxwell-Bloch
system.
|
[
{
"version": "v1",
"created": "Fri, 9 Dec 1994 13:13:14 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Clarkson",
"P. A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Mansfield",
"E. L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Milne",
"A. E.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
]
] |
solv-int/9412004
|
Kenji Kajiwara
|
Kenji Kajiwara(Dept. Electrical Eng., Doshisha Univ.), Yasuhiro
Ohta(Dept. Appl. Math., Fac. Eng., Hiroshima Univ.), and Junkichi
Satsuma(Dept. Math. Sci., Univ. of Tokyo)
|
Casorati Determinant Solutions for the Discrete Painlev\'e III Equation
|
16 pages in LaTeX
| null |
10.1063/1.531353
| null |
solv-int hep-th nlin.SI
| null |
The discrete Painlev\'e III equation is investigated based on the bilinear
formalism. It is shown that it admits the solutions expressed by the Casorati
determinant whose entries are given by the discrete Bessel function. Moreover,
based on the observation that these discrete Bessel functions are transformed
to the $q$-Bessel functions by a simple variable transformation, we present a
$q$-difference analogue of the Painlev\'e III equation.
|
[
{
"version": "v1",
"created": "Thu, 15 Dec 1994 07:47:05 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Kajiwara",
"Kenji",
"",
"Dept. Electrical Eng., Doshisha Univ."
],
[
"Ohta",
"Yasuhiro",
"",
"Dept. Appl. Math., Fac. Eng., Hiroshima Univ."
],
[
"Satsuma",
"Junkichi",
"",
"Dept. Math. Sci., Univ. of Tokyo"
]
] |
solv-int/9412005
| null |
P.G.Grinevich (Landau Institute for Theoretical Physics, Kosygina 2,
Moscow, Russia.), M.U.Schmidt (Institut f\"ur Theoretische Physik, Freie
Universit\"at Berlin, Arnimallee 14 - Berlin, Germany)
|
Period preserving nonisospectral flows and the moduli space of periodic
solutions of soliton equations
|
35 pages, LaTex. Macros file elsart.sty is used (it was submitted by
the authors to [email protected] library macroses),e-mail:
[email protected], e-mail:[email protected]
|
Physica D Nr. 87, pp. 73-98 (1995)
|
10.1016/0167-2789(95)00139-U
| null |
solv-int hep-th nlin.SI
| null |
Flows on the moduli space of the algebraic Riemann surfaces, preserving the
periods of the corresponding solutions of the soliton equations are studied. We
show that these flows are gradient with respect to some indefinite symmetric
flat metric arising in the Hamiltonian theory of the Whitham equations. The
functions generating these flows are conserved quantities for all the equations
simultaneously. We show that for 1+1 systems these flows can be imbedded in a
larger system of ordinary nonlinear differential equations with a rational
right-hand side. Finally these flows are used to give a complete description of
the moduli space of algebraic Riemann surfaces corresponding to periodic
solutions of the nonlinear Schr\"odinger equation.
|
[
{
"version": "v1",
"created": "Thu, 15 Dec 1994 14:11:22 GMT"
},
{
"version": "v2",
"created": "Fri, 16 Dec 1994 20:04:23 GMT"
},
{
"version": "v3",
"created": "Thu, 25 May 1995 10:43:25 GMT"
}
] | 2016-01-19T00:00:00 |
[
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Kosygina 2,\n Moscow, Russia."
],
[
"Schmidt",
"M. U.",
"",
"Institut für Theoretische Physik, Freie\n Universität Berlin, Arnimallee 14 - Berlin, Germany"
]
] |
solv-int/9412006
| null |
Martin U. Schmidt
|
Integrable systems and Riemann surfaces of infinite genus
|
91 page, LaTeX, no pictures
|
Memoirs of the AMS Nr 581 (1996)
| null |
SFB 288/102
|
solv-int hep-th nlin.SI
| null |
To the spectral curves of smooth periodic solutions of the $n$-wave equation
the points with infinite energy are added. The resulting spaces are considered
as generalized Riemann surfcae. In general the genus is equal to infinity,
nethertheless these Riemann surfaces are similar to compact Riemann surfaces.
After proving a Riemann Roch Theorem we can carry over most of the
constructions of the finite gap potentials to all smooth periodic potentials.
The symplectic form turns out to be closely related to Serre duality. Finally
we prove that all non-linear PDE's, which belong to the focussing case of the
non-linear Schr\"odinger equation, have global solutions for arbitrary smooth
periodic inital potantials.
|
[
{
"version": "v1",
"created": "Wed, 21 Dec 1994 19:33:32 GMT"
}
] | 2016-01-19T00:00:00 |
[
[
"Schmidt",
"Martin U.",
""
]
] |
solv-int/9412007
|
Jarmo Niilo Olavi Hietarinta
|
J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta and A. Ramani
|
Bilinear Discrete Painleve-II and its Particular Solutions
|
9 pages in plain TeX
| null |
10.1088/0305-4470/28/12/025
| null |
solv-int nlin.SI
| null |
By analogy to the continuous Painlev\'e II equation, we present particular
solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These
solutions are of rational and special function (Airy) type. Our analysis is
based on the bilinear formalism that allows us to obtain the $\tau$ function
for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained
and we show that they can be related by a simple gauge transformation.
|
[
{
"version": "v1",
"created": "Fri, 23 Dec 1994 12:26:34 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Satsuma",
"J.",
""
],
[
"Kajiwara",
"K.",
""
],
[
"Grammaticos",
"B.",
""
],
[
"Hietarinta",
"J.",
""
],
[
"Ramani",
"A.",
""
]
] |
solv-int/9501001
|
Adam Doliwa
|
Adam Doliwa (Institute of Theoretical Physics, Warsaw University),
Paolo Maria Santini (Dipartimento di Fisica, Universita di Catania and INFN
Sezione di Roma)
|
The Integrable Dynamics of Discrete and Continuous Curves
|
12 pages, LaTeX file, 4 ps figures
| null | null |
Warsaw University IFT 22/94
|
solv-int nlin.SI
| null |
We show that the following geometric properties of the motion of discrete and
continuous curves select integrable dynamics: i) the motion of the curve takes
place in the N dimensional sphere of radius R, ii) the curve does not stretch
during the motion, iii) the equations of the dynamics do not depend explicitly
on the radius of the sphere. Well known examples of integrable evolution
equations, like the nonlinear Schroedinger and the sine-Gordon equations, as
well as their discrete analogues, are derived in this general framework.
|
[
{
"version": "v1",
"created": "Fri, 30 Dec 1994 20:45:31 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
],
[
"Santini",
"Paolo Maria",
"",
"Dipartimento di Fisica, Universita di Catania and INFN\n Sezione di Roma"
]
] |
solv-int/9501002
|
Piotr Grinevich
|
P.G.Grinevich, S.P.Novikov
|
String equation--2. Physical solution
|
32 pages, LaTex, 4 pictures in separate files. Subj-class and
Journal-ref added
|
Algebra and Analysis v. 6 No. 3 (1994) 118-140 (in russian);
english translation -- St. Petersburg Math. J. v. 6 No. 3 (1995) 553-574
| null | null |
solv-int hep-th nlin.SI
| null |
This paper is a continuation of the paper by S.P.Novikov in Funct.Anal.Appl.,
v.24(1990), No 4, pp 196-206. String equation is by definition the equation
$[L,A]=1$ for the coefficients of two linear ordinary differential operators
$L$ and $A$. For the ``double scaling limit'' of the matrix model we always
have $L=-\partial_x^2+u(x)$, $A$ is some differential operator of the odd order
$2k+1$. In the first nontrivial case $k=1$ we have the Painelev\'e-1 (P-1)
equation. Only special real ``separatrix'' solutions of P-1 are important in
the quantum field theory. By the conjecture of Novikov these ``physical''
solutions, which are analytically exceptional probably have much stronger
symmetry then the other solutions but it is not proved until now. Two
asymptotic methods were developed in the previous paper -- nonlinear
semiclassics (or the Bogolubov-Whitham averaging method) and the linear
semiclassics for the ``Isomonodromic'' method. The nonlinear semiclassics gives
a good approximation for the general (``non-physical'') solutions of P-1 but
fails in the ``physical'' case. In our paper the linear semiclasics for the
``physical'' solutions of the P-1 equations is studied. In particular
connection between the semiclassics on Riemann surfaces and Hamiltonian
foliations on these surfaces is established.
|
[
{
"version": "v1",
"created": "Wed, 11 Jan 1995 20:16:04 GMT"
},
{
"version": "v2",
"created": "Fri, 11 Aug 1995 13:58:54 GMT"
},
{
"version": "v3",
"created": "Thu, 20 Apr 2000 15:00:52 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Grinevich",
"P. G.",
""
],
[
"Novikov",
"S. P.",
""
]
] |
solv-int/9501003
|
Fabian Essler
|
Fabian H.L. Essler (Univ. Bonn) and Vladimir E. Korepin (ITP Stony
Brook)
|
Dual Field Approach to Correlation Functions in the Heisenberg Xxz Spin
Chain
|
19 pages LaTeX, to appear in the proceedings of SMQFT, Los Angeles
1994
| null | null | null |
solv-int nlin.SI
| null |
We study zero temperature correlation functions of the spin-$1\over 2$
Heisenberg XXZ model in the critical regime $-1< \Delta\leq 1$ in a magnetic
field by means of the {\tenit Dual Field Approach}. We show for one particular
example how to derive determinant representations for correlation functions and
how to use these to embed the correlation functions in integrable systems of
integro-difference equations (IDE). These IDE are associated with a
Riemann-Hilbert problem.
|
[
{
"version": "v1",
"created": "Wed, 11 Jan 1995 23:10:09 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Essler",
"Fabian H. L.",
"",
"Univ. Bonn"
],
[
"Korepin",
"Vladimir E.",
"",
"ITP Stony\n Brook"
]
] |
solv-int/9501004
|
Mark Mineev
|
Mark B. Mineev-Weinstein
|
Conservation Laws in Field Dynamics or Why Boundary Motion is Exactly
Integrable?
|
LaTeX file, 12 pages
| null | null | null |
solv-int nlin.SI
| null |
An infinite number of conserved quantities in the field dynamics $\phi_t = L
U(\phi) + \rho$ for a linear Hermitian (or anti-Hermitian) operator $L$, an
arbitrary function $U$ and a given source $\rho$ are presented. These integrals
of motion are the multipole moments of the potential created by $\phi$ in the
far-field. In the singular limit of a bistable scalar field $\phi = \phi_{\pm}$
(i.e. Ising limit) this theory describes a dissipative boundary motion (such as
Stefan or Saffman-Taylor problem that is the continuous limit of the
DLA-fractal growth) and can be exactly integrable. These conserved quantities
are the polynomial conservation laws attributed to the integrability. The
criterion for integrability is the uniqueness of the inverse potential
problem's solution.
|
[
{
"version": "v1",
"created": "Wed, 11 Jan 1995 23:32:14 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Mineev-Weinstein",
"Mark B.",
""
]
] |
solv-int/9501005
|
Saburo Kakei
|
Saburo Kakei, Narimasa Sasa and Junkichi Satsuma
|
Bilinearization of a Generalized Derivative Nonlinear Schr\"odinger
equation
|
7 pages, LaTeX file, no figures
|
J. Phys. Soc. Jpn. 64 (1995) 1519
|
10.1143/JPSJ.64.1519
| null |
solv-int nlin.SI
| null |
A generalized derivative nonlinear Schr\"odinger equation,
\ii q_t + q_{xx} + 2\ii \gamma |q|^2 q_x + 2\ii (\gamma-1)q^2 q^*_x +
(\gamma-1)(\gamma-2)|q|^4 q = 0 ,
is studied by means of Hirota's bilinear formalism. Soliton solutions are
constructed as quotients of Wronski-type determinants. A relationship between
the bilinear structure and gauge transformation is also discussed.
|
[
{
"version": "v1",
"created": "Tue, 17 Jan 1995 08:42:01 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Kakei",
"Saburo",
""
],
[
"Sasa",
"Narimasa",
""
],
[
"Satsuma",
"Junkichi",
""
]
] |
solv-int/9501006
| null |
P.G.Grinevich & S.P.Novikov
|
Nonselfintersecting magnetic orbits on the plane. Proof of Principle of
the Overthrowing of the Cycles.
|
33 pages, LaTeX.
|
Transl. of Amer. Math. Soc. series 2 v 170 (1995) 199-206
| null | null |
solv-int hep-th nlin.SI
| null |
Beginning from 1981 one of the present authors (S.Novikov) published a series
of papers, (some of them in collaboration with I.Schmelzer and I.Taimanov)
dedicated to the development of the analog of Morse theory for the closed
1-forms -- multivalued functions and functionals -- on the finite - and
infinite-dimensional manifolds ({\bf Morse-Novikov Theory}).
The notion of ``Multivalued action'' was understood and ``Topological
quantization of the coupling constant'' for them was formulated by Novikov in
1981 as a Corollary from the requirement, that the Feinmann Amplitude should be
one-valued on the space of fields-maps. Very beautiful analog of this theory
appeared also in the late 80-ies in the Symplectic Geometry and Topology, when
the so-called Floer Homology Theory was discovered. A very first topological
idea of this theory, formulated in early 80-ies, was the so-called ``Principle
of the Overthrowing of the Cycles''. It led to the results which were not
proved rigorously until now. Our goal is to prove some of them.
We study the motion of a classical charged particle on the Euclidean plane in
a magnetic field orthogonal to this field. The trajectories of this motion can
be characterized as extremals of the ``Maupertui--Fermat'' functional. We show
that for any smooth everyvhere positive double periodic magnetic field for any
fixed energy there exist at least two different periodic convex extremals, such
that the value of the Maupertui-Fermat functional is positive for them. If all
such extremals are nondegenerate in the sense of Morse in the space of
nonparameterized curves then for any energy there exist at least 4 periodic
convex extremals with the Morse indices (1,2,2,3).
|
[
{
"version": "v1",
"created": "Wed, 18 Jan 1995 11:07:58 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Grinevich",
"P. G.",
""
],
[
"Novikov",
"S. P.",
""
]
] |
solv-int/9501007
|
Leonid Vitalevich Bogdanov
|
L.V. Bogdanov (IINS, Landau Institute for Theoretical Physics,
Russia), B.G. Konopelchenko (Dipartimento di Fisica dell'Universit\`a, Lecce,
Italy)
|
Lattice and q-difference Darboux-Zakharov-Manakov systems via
$\bar{\partial}$-dressing method
|
8 pages, LaTeX, to be published in J Phys A, Letters.
| null |
10.1088/0305-4470/28/5/005
| null |
solv-int math.QA nlin.SI q-alg
| null |
A general scheme is proposed for introduction of lattice and q-difference
variables to integrable hierarchies in frame of $\bar{\partial}$-dressing
method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov
systems of equations are derived. Darboux, B\"acklund and Combescure
transformations and exact solutions for these systems are studied.
|
[
{
"version": "v1",
"created": "Sat, 28 Jan 1995 03:53:19 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Bogdanov",
"L. V.",
"",
"IINS, Landau Institute for Theoretical Physics,\n Russia"
],
[
"Konopelchenko",
"B. G.",
"",
"Dipartimento di Fisica dell'Università, Lecce,\n Italy"
]
] |
solv-int/9501008
| null |
E. Alfinito, M. Leo, R.A. Leo, M. Palese and G. Soliani
|
Integrable nonlinear field equations and loop algebra structures
|
13 pages, latex, no figures,
|
Phys. Lett. B352, 314 (1995)
|
10.1016/0370-2693(95)00561-X
| null |
solv-int cond-mat hep-th nlin.SI
| null |
We apply the (direct and inverse) prolongation method to a couple of
nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field
model for analyzing the existence of a connection between the integrability
property and loop algebras. Exploiting a realization of the Kac-Moody type of
the incomplete prolongation algebra associated with the system under
consideration, we develop a procedure with allows us to generate a new class of
integrable nonlinear field equations containing the original ones as a special
case.
|
[
{
"version": "v1",
"created": "Mon, 30 Jan 1995 15:12:44 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Alfinito",
"E.",
""
],
[
"Leo",
"M.",
""
],
[
"Leo",
"R. A.",
""
],
[
"Palese",
"M.",
""
],
[
"Soliani",
"G.",
""
]
] |
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