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| versions
list | update_date
timestamp[s] | authors_parsed
list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
solv-int/9501009
|
Chris Jarzynski
|
Christopher Jarzynski
|
Geometric phase effects for wavepacket revivals
|
Revtex, 11 pages, no figures.
|
Phys.Rev.Lett. 74 (1995) 1264
|
10.1103/PhysRevLett.74.1264
|
DOE/ER/40561-180-INT94-14-03
|
solv-int nlin.SI quant-ph
| null |
The study of wavepacket revivals is extended to the case of Hamiltonians
which are made time-dependent through the adiabatic cycling of some parameters.
It is shown that the quantal geometric phase (Berry's phase) causes the revived
packet to be displaced along the classical trajectory, by an amount equal to
the classical geometric phase (Hannay's angle), in one degree of freedom. A
physical example illustrating this effect in three degrees of freedom is
mentioned.
|
[
{
"version": "v1",
"created": "Thu, 2 Feb 1995 22:23:17 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Jarzynski",
"Christopher",
""
]
] |
solv-int/9502001
|
Jarmo Hietarinta
|
J. Hietarinta, T. Kuusela and B. Malomed
|
Shock waves in the dissipative Toda lattice
|
10 pages in LaTeX, 5 figures available upon reguest
| null |
10.1088/0305-4470/28/11/007
| null |
solv-int nlin.SI
| null |
We consider the propagation of a shock wave (SW) in the damped Toda lattice.
The SW is a moving boundary between two semi-infinite lattice domains with
different densities. A steadily moving SW may exist if the damping in the
lattice is represented by an ``inner'' friction, which is a discrete analog of
the second viscosity in hydrodynamics. The problem can be considered
analytically in the continuum approximation, and the analysis produces an
explicit relation between the SW's velocity and the densities of the two
phases. Numerical simulations of the lattice equations of motion demonstrate
that a stable SW establishes if the initial velocity is directed towards the
less dense phase; in the opposite case, the wave gradually spreads out. The
numerically found equilibrium velocity of the SW turns out to be in a very good
agreement with the analytical formula even in a strongly discrete case. If the
initial velocity is essentially different from the one determined by the
densities (but has the correct sign), the velocity does not significantly
alter, but instead the SW adjusts itself to the given velocity by sending
another SW in the opposite direction.
|
[
{
"version": "v1",
"created": "Fri, 3 Feb 1995 10:00:30 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Hietarinta",
"J.",
""
],
[
"Kuusela",
"T.",
""
],
[
"Malomed",
"B.",
""
]
] |
solv-int/9502002
|
Richard Ward
|
R. S. Ward
|
Discrete Toda Field Equations
|
7 pages, plainTeX
| null |
10.1016/0375-9601(95)00108-F
|
DTP/95/3; NI94031
|
solv-int hep-th nlin.SI
| null |
There are two-dimensional Toda field equations corresponding to each (finite
or affine) Lie algebra. The question addressed in this note is whether there
exist integrable discrete versions of these. It is shown that for certain
algebras (such as $A_n$, $A_n^{(1)}$ and $B_n$) there do, but some of these
systems are defined on the half-plane rather than the full two-dimensional
lattice.
|
[
{
"version": "v1",
"created": "Wed, 8 Feb 1995 14:37:15 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Ward",
"R. S.",
""
]
] |
solv-int/9502003
|
David Fairlie
|
D.B. Fairlie and I.A.B. Strachan
|
The Hamiltonian structure of the dispersionless Toda hierarchy
|
12 pages, latex, no figures
|
Physica D: Vol 90, Issues 1-2 (1996), 1-8
|
10.1016/0167-2789(95)00229-4
|
DTP/95/5
|
solv-int nlin.SI
| null |
The Hamiltonian structure of the two-dimensional dispersionless Toda
hierarchy is studied, this being a particular example of a system of
hydrodynamic type. The polynomial conservation laws for the system turn out,
after a change of variable, to be associated with the axially symmetric
solutions of the 3-dimensional Laplace equation and this enables a generating
function for the Hamiltonian densities to be derived in closed form.
|
[
{
"version": "v1",
"created": "Mon, 13 Feb 1995 16:41:01 GMT"
}
] | 2020-12-16T00:00:00 |
[
[
"Fairlie",
"D. B.",
""
],
[
"Strachan",
"I. A. B.",
""
]
] |
solv-int/9502004
|
Piotr Goldstein
|
Jan Cie\'sli\'nski (Warsaw University Division in Bia{\l}ystok,
Institute of Physics, Bia{\l}ystok, Poland), Piotr Goldstein (Soltan
Institute for Nuclear Studies, Warsaw, Poland), and Antoni Sym (Warsaw
University, Institute of Theoretical Physics, Warsaw, Poland)
|
Isothermic surfaces in $\E^3$ as soliton surfaces
|
Revised version; 13 pages in LaTeX, 1 figure PostScript; to appear in
Physics Letters A
| null |
10.1016/0375-9601(95)00504-V
| null |
solv-int dg-ga math.DG nlin.SI
| null |
We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest
branches of differential geometry -- can be reformulated within the modern
theory of completely integrable (soliton) systems. This enables one to study
the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral
methods available in the soliton theory. Also the associated non-linear system
is interesting in itself since it displays some unconventional soliton features
and, physically, could be applied in the theory of infinitesimal deformations
of membranes.
|
[
{
"version": "v1",
"created": "Tue, 14 Feb 1995 18:53:01 GMT"
},
{
"version": "v2",
"created": "Thu, 20 Jul 1995 16:40:19 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Cieśliński",
"Jan",
"",
"Warsaw University Division in Białystok,\n Institute of Physics, Białystok, Poland"
],
[
"Goldstein",
"Piotr",
"",
"Soltan\n Institute for Nuclear Studies, Warsaw, Poland"
],
[
"Sym",
"Antoni",
"",
"Warsaw\n University, Institute of Theoretical Physics, Warsaw, Poland"
]
] |
solv-int/9502005
|
Benzion Shklyar
|
B. Shklyar (Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel)
|
On The Observability For Distributed Systems By Means Of Linear
Operations
|
20 pages, LaTeX
| null | null |
bimacs-95
|
solv-int nlin.SI
| null |
An observability problem for linear autonomous distributed systems in the
class of linear operations is considered. A criterion of observability with
respect to terminal state has been proved. A connection with observability with
respect to initial state is discussed.
|
[
{
"version": "v1",
"created": "Thu, 16 Feb 1995 18:02:55 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Shklyar",
"B.",
"",
"Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel"
]
] |
solv-int/9502006
|
Yuji Kodama
|
Y. Kodama, and K. T-R McLaughlin
|
Explicit Integration of the Full Symmetric Toda Hierarchy and the
Sorting Property
|
13 pages, Latex.
| null |
10.1007/BF00400137
| null |
solv-int nlin.SI
| null |
We give an explicit formula for the solution to the initial value problem of
the full symmetric Toda hierarchy. The formula is obtained by the
orthogonalization procedure of Szeg\"{o}, and is also interpreted as a
consequence of the QR factorization method of Symes \cite{symes}. The sorting
property of the dynamics is also proved for the case of a generic symmetric
matrix in the sense described in the text, and generalizations of tridiagonal
formulae are given for the case of matrices with $2M+1$ nonzero diagonals.
|
[
{
"version": "v1",
"created": "Wed, 22 Feb 1995 17:49:48 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Kodama",
"Y.",
""
],
[
"McLaughlin",
"K. T-R",
""
]
] |
solv-int/9503001
|
Liu Qing-ping
|
Q.P. Liu
|
Supersymmetric Harry Dym Type Equations
|
4 pages, latex, no figures
| null |
10.1088/0305-4470/28/8/004
|
CUMT-MATH-95-01
|
solv-int nlin.SI
| null |
A supersymmetric version is proposed for the well known Harry Dym system. A
general class super Lax operator which leads to consistent equations is
considered.
|
[
{
"version": "v1",
"created": "Fri, 17 Mar 1995 16:25:25 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Liu",
"Q. P.",
""
]
] |
solv-int/9503002
|
Leon Jerome
|
C. Claude and J. Leon (Physique Mathematique et Theorique, CNRS-URA
768, Universite Montpellier II, 34095 MONTPELLIER FRANCE)
|
Theory of Pump Depletion and Spike Formation in Stimulated Raman
Scattering
|
LaTex file, includes two figures in LaTex format, 9 pages
| null |
10.1103/PhysRevLett.74.3479
|
PM 94-16
|
solv-int nlin.PS nlin.SI patt-sol
| null |
By using the inverse spectral transform, the SRS equations are solved and the
explicit output data is given for arbitrary laser pump and Stokes seed profiles
injected on a vacuum of optical phonons. For long duration laser pulses, this
solution is modified such as to take into account the damping rate of the
optical phonon wave. This model is used to interprete the experiments of Druhl,
Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular
the creation of a spike of (anomalous) pump radiation. The related nonlinear
Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike
is not a soliton.
|
[
{
"version": "v1",
"created": "Fri, 17 Mar 1995 10:41:45 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Claude",
"C.",
"",
"Physique Mathematique et Theorique, CNRS-URA\n 768, Universite Montpellier II, 34095 MONTPELLIER FRANCE"
],
[
"Leon",
"J.",
"",
"Physique Mathematique et Theorique, CNRS-URA\n 768, Universite Montpellier II, 34095 MONTPELLIER FRANCE"
]
] |
solv-int/9503003
|
Denis V. Juriev
|
Denis V.Juriev
|
On the dynamics of noncanonically coupled oscillators and its hidden
superstructure
|
revised version -- refs are updated
| null | null |
ESI-167
|
solv-int nlin.SI
| null |
The classical and quantum dynamics of the noncanonically coupled oscillators
is considered. It is shown that though the classical dynamics is well--defined
for both harmonic and anharmonic oscillators, the quantum one is well--defined
in the harmonic case, admits a hidden (super)Hamiltonian formulation, and thus,
preserves the initial operator relations, whereas a na\"\i ve quantization of
the anharmonic case meets with principal difficulties.
|
[
{
"version": "v1",
"created": "Sat, 25 Mar 1995 10:31:03 GMT"
},
{
"version": "v2",
"created": "Sun, 6 Aug 1995 05:50:07 GMT"
},
{
"version": "v3",
"created": "Thu, 4 Apr 1996 04:59:30 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Juriev",
"Denis V.",
""
]
] |
solv-int/9504001
|
Evgenii Sklyanin
|
E.K. Sklyanin
|
Separation of Variables. New Trends.
|
33 pages, harvmac, no figures
|
Prog.Theor.Phys.Suppl.118:35-60,1995
|
10.1143/PTPS.118.35
|
UTMS 95-9
|
solv-int nlin.SI
| null |
The review is based on the author's papers since 1985 in which a new approach
to the separation of variables (\SoV) has being developed. It is argued that
\SoV, understood generally enough, could be the most universal tool to solve
integrable models of the classical and quantum mechanics. It is shown that the
standard construction of the action-angle variables from the poles of the
Baker-Akhiezer function can be interpreted as a variant of \SoV, and moreover,
for many particular models it has a direct quantum counterpart. The list of the
models discussed includes XXX and XYZ magnets, Gaudin model, Nonlinear
Schr\"odinger equation, $SL(3)$-invariant magnetic chain. New results for the
3-particle quantum Calogero-Moser system are reported.
|
[
{
"version": "v1",
"created": "Tue, 4 Apr 1995 09:34:27 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Sklyanin",
"E. K.",
""
]
] |
solv-int/9504002
|
Costas Efthimiou
|
S. A. APIKYAN (Yerevan Physics Institute) and C. J. EFTHIMIOU (Cornell
University)
|
$V_{(1,1)}^{(t)}$-PERTURBED MODELS OF CFT AND THEIR QUANTUM GROUP
SYMMETRY
|
16 pages, LaTeX file, AMS fonts
|
Phys.Lett. B359 (1995) 313-320
|
10.1016/0370-2693(95)01075-2
|
Cornell preprint CLNS 95/1330
|
solv-int hep-th nlin.SI
| null |
We propose a new massive integrable model in quantum field theory. This model
is obtained as a perturbed model of the minimal conformal field theories on the
hyper-elliptic surfaces by a particular relavant operator $V_{(1,1)}^{(t)}$.
The non-local conserved charges of the model and their $q$-deformed algebra are
also constructed explicitly.
|
[
{
"version": "v1",
"created": "Wed, 5 Apr 1995 23:57:10 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"APIKYAN",
"S. A.",
"",
"Yerevan Physics Institute"
],
[
"EFTHIMIOU",
"C. J.",
"",
"Cornell\n University"
]
] |
solv-int/9504003
|
Liu Qing-ping
|
Q.P. Liu
|
Painlev\'{e} Analysis and Exact Solutions of a Modified Boussinesq
Equation
|
7 pages, LaTeX file
| null | null |
CUMT-Math-9504
|
solv-int nlin.SI
| null |
We consider a modified Boussinesq type equation. The Painlev\'{e} test of the
WTC method is performed for this equation and it shows that the equation has
weak Painlev\'{e} property. Some exact solutions are constructed.
|
[
{
"version": "v1",
"created": "Thu, 27 Apr 1995 15:44:46 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Liu",
"Q. P.",
""
]
] |
solv-int/9505001
|
Denis V. Juriev
|
Denis V. Juriev
|
Topics in nonhamiltonian (magnetic-type) interaction of classical
hamiltonian dynamical systems. I
|
AMSTEX 9 pages, a slightly revised version
|
Russian J.Math.Phys.3(4)(1995)
| null | null |
solv-int nlin.SI
| null |
A convenient algebraic structure to describe some forms of dynamics of two
hamiltonian systems with nonpotential (magnetic--type) interaction is
considered. An algebraic mechanism of generation of such dynamics is explored
on simple "toy" examples and models. Nonpotential chains and their continuum
limits are also considered. Examples of hybrid couplings with both potential
and nonpotential (magnetic--type) interactions are discussed.
|
[
{
"version": "v1",
"created": "Fri, 5 May 1995 12:46:52 GMT"
},
{
"version": "v2",
"created": "Sun, 6 Aug 1995 00:55:33 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Juriev",
"Denis V.",
""
]
] |
solv-int/9505002
|
Andrzej Maciejewski
|
Andrzej J.~Maciejewski (Institute of Astronomy, N. Copernicus
University, Chopina 12-18, 87-100 Toru\'n, Poland), Jean-Marie Strelcyn
(D\'epartement de Math\'ematiques, Universit\'e de Rouen,76821 Mont Saint
Aignan Cedex, France, URA CNRS 1378)
|
On the algebraic non-integrability of the Halphen system
|
10 pages, AMSLaTeX, to appear in Physics Letters A
| null | null | null |
solv-int nlin.SI
| null |
It is proved that the Halphen system of ordinary differential equations has
no non-trivial rational first integrals.
|
[
{
"version": "v1",
"created": "Fri, 12 May 1995 16:17:23 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"~Maciejewski",
"Andrzej J.",
"",
"Institute of Astronomy, N. Copernicus\n University, Chopina 12-18, 87-100 Toruń, Poland"
],
[
"Strelcyn",
"Jean-Marie",
"",
"Département de Mathématiques, Université de Rouen,76821 Mont Saint\n Aignan Cedex, France, URA CNRS 1378"
]
] |
solv-int/9505003
|
Adler
|
V.E. Adler and I.T. Habibullin (Ufa Institute of Mathematics, Russian
Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia)
|
Integrable boundary conditions for the Toda lattice
| null | null |
10.1088/0305-4470/28/23/021
| null |
solv-int nlin.SI
| null |
The problem of construction of the boundary conditions for the Toda lattice
compatible with its higher symmetries is considered. It is demonstrated that
this problem is reduced to finding of the differential constraints consistent
with the ZS-AKNS hierarchy. A method of their construction is offered based on
the B\"acklund transformations. It is shown that the generalized Toda lattices
corresponding to the non-exceptional Lie algebras of finite growth can be
obtained by imposing one of the four simplest integrable boundary conditions on
the both ends of the lattice. This fact allows, in particular, to solve the
problem of reduction of the series $A$ Toda lattices into the series $D$ ones.
Deformations of the found boundary conditions are presented which leads to the
Painlev\'e type equations.
Key words: Toda lattice, boundary conditions, integrability, B\"acklund
transformation, Lie algebras, Painlev\'e equations
|
[
{
"version": "v1",
"created": "Wed, 17 May 1995 03:00:01 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Adler",
"V. E.",
"",
"Ufa Institute of Mathematics, Russian\n Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia"
],
[
"Habibullin",
"I. T.",
"",
"Ufa Institute of Mathematics, Russian\n Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia"
]
] |
solv-int/9505004
|
Yuji Kodama
|
Yuji Kodama, and Jian Ye
|
Toda Hierarchy with Indefinite Metric
|
26 pages, LaTeX
| null |
10.1016/0167-2789(95)00269-3
| null |
solv-int hep-th nlin.SI
| null |
We consider a generalization of the full symmetric Toda hierarchy where the
matrix $\tilde {L}$ of the Lax pair is given by $\tilde {L}=LS$, with a full
symmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature
of the hierarchy is that the inverse scattering data includes a class of
noncompact groups of matrices, such as $O(p,q)$. We give an explicit formula
for the solution to the initial value problem of this hierarchy. The formula is
obtained by generalizing the orthogonalization procedure of Szeg\"{o}, or the
QR factorization method of Symes. The behaviors of the solutions are also
studied. Generically, there are two types of solutions, having either sorting
property or blowing up to infinity in finite time. The $\tau$-function
structure for the tridiagonal hierarchy is also studied.
|
[
{
"version": "v1",
"created": "Fri, 19 May 1995 15:17:21 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Kodama",
"Yuji",
""
],
[
"Ye",
"Jian",
""
]
] |
solv-int/9505005
|
Latypov A. M.
|
Azat M.Latypov (Fluid Dynamics Research Institute and Department of
Mathematics and Statistics, University of Windsor, CANADA)
|
Approximate Lie Group Analysis of a Model Advection Equation on an
Unstructured Grid
|
8 pages, LaTeX
| null | null | null |
solv-int comp-gas nlin.CG nlin.SI
| null |
A technique of ``approximate group analysis'' recently developed by Baikov,
Gazizov and Ibragimov is applied to a differential approximation (otherwise
referred to as an equivalent differential equation) corresponding to the finite
difference approximation of a nonlinear advection equation on unstructured
grid. We determine which groups from the infinite variety of groups admitted by
a nonlinear advection equation ``survive'' the discretization. The situations
arising for different choices of an arbitrary function (local speed of
propagation) are also studied.
|
[
{
"version": "v1",
"created": "Tue, 30 May 1995 07:14:16 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Latypov",
"Azat M.",
"",
"Fluid Dynamics Research Institute and Department of\n Mathematics and Statistics, University of Windsor, CANADA"
]
] |
solv-int/9505006
| null |
R.Z.Zhdanov
|
Conditional Lie-B\"acklund symmetry and reduction of evolution
equations.
|
12 pages, latex, needs amssymb., to appear in the "Journal of Physics
A: Mathematical and General" (1995)
| null |
10.1088/0305-4470/28/13/027
| null |
solv-int nlin.SI
| null |
We suggest a generalization of the notion of invariance of a given partial
differential equation with respect to Lie-B\"acklund vector field. Such
generalization proves to be effective and enables us to construct principally
new Ans\"atze reducing evolution-type equations to several ordinary
differential equations. In the framework of the said generalization we obtain
principally new reductions of a number of nonlinear heat conductivity equations
$u_t=u_{xx}+F(u,u_x)$ with poor Lie symmetry and obtain their exact solutions.
It is shown that these solutions can not be constructed by means of the
symmetry reduction procedure.
|
[
{
"version": "v1",
"created": "Wed, 31 May 1995 06:50:33 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Zhdanov",
"R. Z.",
""
]
] |
solv-int/9506001
|
Hikami Kazuhiro
|
Kazuhiro Hikami
|
Separation of Variables in BC-type Gaudin Magnet
|
11 pages, macros from ftp.ioppublishing.com
| null |
10.1088/0305-4470/28/14/023
| null |
solv-int nlin.SI
| null |
The integrable system is introduced based on the Poisson $ rs $-matrix
structure. This is a generalization of the Gaudin magnet, and in SL(2) case
isomorphic to the generalized Neumann model. The separation of variables is
discussed for both classical and quantum case.
|
[
{
"version": "v1",
"created": "Wed, 7 Jun 1995 11:29:16 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Hikami",
"Kazuhiro",
""
]
] |
solv-int/9506002
|
Daniel Finley
|
J. D. Finley, III, John K. McIver (University of New Mexico)
|
Infinite-Dimensional Estabrook-Wahlquist Prolongations for the
sine-Gordon Equation
|
46 pages, plain TeX, no figures, to be published in J. Math. Phys.
| null |
10.1063/1.531348
| null |
solv-int nlin.SI
| null |
We are looking for the universal covering algebra for all symmetries of a
given pde, using the sine-Gordon equation as a typical example for a
non-evolution equation. For non-evolution equations, Estabrook-Wahlquist
prolongation structures for non-local symmetries depend on the choice of a
specific sub-ideal, of the contact module, to define the pde. For each
inequivalent such choice we determine the most general solution of the
prolongation equations, as sub-algebras of the (infinite-dimensional) algebra
of all vector fields over the space of non-local variables associated with the
pde, in the style of Vinogradov covering spaces. We show explicitly how
previously-known prolongation structures, known to lie within the Kac-Moody
algebra, $A_1^{(1)}$, are special cases of these general solutions, although we
are unable to identify the most general solutions with previously-studied
algebras. We show the existence of gauge transformations between prolongation
structures, viewed as determining connections over the solution space, and use
these to relate (otherwise) distinct algebras. Faithful realizations of the
universal algebra allow integral representations of the prolongation structure,
opening up interesting connections with algebras of Toeplitz operators over
Banach spaces, an area that has only begun to be explored.
|
[
{
"version": "v1",
"created": "Fri, 9 Jun 1995 19:27:54 GMT"
}
] | 2012-08-27T00:00:00 |
[
[
"Finley",
"J. D.",
"",
"University of New Mexico"
],
[
"III",
"",
"",
"University of New Mexico"
],
[
"McIver",
"John K.",
"",
"University of New Mexico"
]
] |
solv-int/9506003
|
Igor Germanovich Korepanov
|
I.G. Korepanov
|
Algebraic integrable dynamical systems, 2+1-dimensional models in wholly
discrete space-time, and inhomogeneous models in 2-dimensional statistical
physics
|
1) Normally, this must be LaTeXed 3 times! (I beg your pardon) 2)
your TeX system must include the \special{em: ...} commands to get the
pictures properly, 3) even if it does, one figure is missing--you will see an
empty space of height about 8 cm, with a caption below it. Please contact the
author
| null | null | null |
solv-int nlin.SI
| null |
This paper is devoted to constructing and studying exactly solvable dynamical
systems in discrete time obtained from some algebraic operations on matrices,
to reductions of such systems leading to classical field theory models in
2+1-dimensional wholly discrete space-time, and to connection between those
field theories and inhomogoneous models in 2-dimensional statistical physics.
|
[
{
"version": "v1",
"created": "Sat, 1 Jul 1995 12:36:58 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9506004
|
Adam Doliwa
|
Adam Doliwa (Institute of Theoretical Physics, Warsaw University)
|
Holomorphic Curves and Toda Systems
|
14 pages, LaTeX (minor spelling changes)
|
Lett. Math. Phys. 39 (1997) 21
|
10.1007/s11005-997-1032-7
|
IFT 7/95
|
solv-int alg-geom dg-ga math.AG math.DG nlin.SI
| null |
Geometry of holomorphic curves from point of view of open Toda systems is
discussed. Parametrization of curves related this way to non-exceptional simple
Lie algebras is given. This gives rise to explicit formulas for minimal
surfaces in real, complex and quaternionic projective spaces or complex
quadrics. The paper generalizes the well known connection between minimal
surfaces in $\EE^{3}$, their Weierstrass representation in terms of holomorphic
functions and the general solution to the Liouville equation.
|
[
{
"version": "v1",
"created": "Mon, 3 Jul 1995 15:37:43 GMT"
},
{
"version": "v2",
"created": "Tue, 4 Jul 1995 12:38:09 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
]
] |
solv-int/9506005
|
Yuji Kodama
|
Yuji Kodama and Jian Ye
|
Iso-spectral deformations of general matrix and their reductions on Lie
algebras
|
25 pages, AMSLaTex
| null |
10.1007/BF02108824
| null |
solv-int hep-th nlin.SI
| null |
We study an iso-spectral deformation of general matrix which is a natural
generalization of the Toda lattice equation. We prove the integrability of the
deformation, and give an explicit formula for the solution to the initial value
problem. The formula is obtained by generalizing the orthogonalization
procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we
consider several reductions of the hierarchy. These include not only the
integrable systems studied by Bogoyavlensky and Kostant, but also their
generalizations which were not known to be integrable before. The behaviors of
the solutions are also studied. Generically, there are two types of solutions,
having either sorting property or blowing up to infinity in finite time.
|
[
{
"version": "v1",
"created": "Mon, 3 Jul 1995 18:15:34 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Kodama",
"Yuji",
""
],
[
"Ye",
"Jian",
""
]
] |
solv-int/9506006
|
Craig A. Tracy
|
Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz)
|
Fredholm determinants and the mKdV/sinh-Gordon hierarchies
|
11 pages, LaTeX file, no figures
|
Commun. Math. Phys 179 (1996) 1--9
|
10.1007/BF02103713
| null |
solv-int hep-th math-ph math.MP nlin.SI
| null |
For a particular class of integral operators $K$ we show that the quantity
\[\ph:=\log \det (I+K)-\log \det (I-K)\] satisfies both the integrated mKdV
hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of
Zamolodchikov.
|
[
{
"version": "v1",
"created": "Fri, 7 Jul 1995 01:17:41 GMT"
}
] | 2009-07-11T00:00:00 |
[
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9507001
|
Costas Efthimiou
|
Costas J. Efthimiou (Cornell University) and Samwel A. Apikyan
(Yerevan Physics Insitute)
|
Integrable Models on Hyper-Elliptic Surfaces
|
uuencoded Z-compressed postscript file
| null | null |
Cornell Preprint CLNS 95/1342
|
solv-int hep-th nlin.SI
| null |
We present an elementary introduction to the construction of integrable
models on hyper-elliptic surfaces for non specialists; also, we present some of
the details of the paper `solv-int/9504002' for the more interested readers.
(Based on a talk given at the MRST 95 meeting by C. E.)
|
[
{
"version": "v1",
"created": "Wed, 12 Jul 1995 23:04:33 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Efthimiou",
"Costas J.",
"",
"Cornell University"
],
[
"Apikyan",
"Samwel A.",
"",
"Yerevan Physics Insitute"
]
] |
solv-int/9507002
|
Jan Felipe van Diejen
|
J. F. van Diejen
|
Multivariable continuous Hahn and Wilson polynomials related to
integrable difference systems
|
5 pages, REVTEX, to appear in J. Phys. A: Math. Gen
|
J. Phys. A: Math. Gen. 28 (1995) L369-74
|
10.1088/0305-4470/28/13/003
| null |
solv-int nlin.SI
| null |
Multivariable generalizations of the continuous Hahn and Wilson polynomials
are introduced as eigenfunctions of rational Ruijsenaars type difference
systems with an external field.
|
[
{
"version": "v1",
"created": "Wed, 19 Jul 1995 10:00:54 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"van Diejen",
"J. F.",
""
]
] |
solv-int/9507003
| null |
Renat Z. Zhdanov, Ihor V. Revenko and Wilhelm I. Fushchych
|
On the new approach to variable separation in the time-dependent
Schr\"odinger equation with two space dimensions
|
21 pages, latex, to appear in the "Journal of Mathematical Physics"
(1995)
| null |
10.1063/1.531274
| null |
solv-int hep-ph nlin.SI
| null |
We suggest an effective approach to separation of variables in the
Schr\"odinger equation with two space variables. Using it we classify
inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger
equations admit separation of variables. Besides that, we carry out separation
of variables in the Schr\" odinger equation with the anisotropic harmonic
oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of
coordinate systems providing its separability. Most of these coordinate systems
depend essentially on the form of the potential and do not provide separation
of variables in the free Schr\" odinger equation ($V=0$).
|
[
{
"version": "v1",
"created": "Thu, 20 Jul 1995 07:46:02 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Zhdanov",
"Renat Z.",
""
],
[
"Revenko",
"Ihor V.",
""
],
[
"Fushchych",
"Wilhelm I.",
""
]
] |
solv-int/9507004
|
G. Tondo
|
G. Tondo (Dipartimento di Scienze Matematiche, Universita degli Studi
di Trieste)
|
On the integrability of stationary and restricted flows of the KdV
hierarchy.
|
25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A:
Math. Gen..
| null |
10.1088/0305-4470/28/17/034
| null |
solv-int nlin.SI
| null |
A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is
derived in an extended phase space. A map between stationary flows and
restricted flows is constructed: in a case it connects an integrable
Henon--Heiles system and the Garnier system. Moreover a new integrability
scheme for Hamiltonian systems is proposed, holding in the standard phase
space.
|
[
{
"version": "v1",
"created": "Sat, 22 Jul 1995 14:26:49 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Tondo",
"G.",
"",
"Dipartimento di Scienze Matematiche, Universita degli Studi\n di Trieste"
]
] |
solv-int/9507005
|
Nagesha N. Rao
|
N.N. Rao (Theoretical Physics Division, Physical Research Laboratory,
Navrangpura, Ahmedabad-380009, India)
|
Henon-Heiles Hamiltonian for Coupled Upper-Hybrid and Magnetoacoutic
Waves in Magnetized Plasmas
|
11 pages; Latex file, Two figures upon request submitted to the
Journal, appeared in Phys. Letts., A202, 383 (1995)
| null |
10.1016/0375-9601(95)00361-6
|
PRL-TH/95-5;
|
solv-int nlin.SI
| null |
We show that the coupled mode equations for the stationary propagation of
upper--hybrid and magnetoacoustic waves in magnetized electron--ion plasmas
with negative group dispersion can be exactly derived from the generalized
\Henon--Heiles Hamiltonian. The parameter regimes for the integrable cases of
the coupled mode equations have been explicitly obtained. For positive group
dispersion of the upper--hybrid waves, the relevant governing equations lead to
a novel Hamiltonian where the kinetic energy is not positive definite.
|
[
{
"version": "v1",
"created": "Mon, 24 Jul 1995 06:03:19 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Rao",
"N. N.",
"",
"Theoretical Physics Division, Physical Research Laboratory,\n Navrangpura, Ahmedabad-380009, India"
]
] |
solv-int/9507006
| null |
A. Zujewski
|
Hamiltonian Structures on Coadjoint Orbits of Semidirect Product of
$G=Diff_+(S^{1})$ and $C^{\infty}(S^1, {\bf R})$
|
17 pages, LaTeX
| null | null | null |
solv-int hep-th nlin.SI
| null |
We consider the semidirect product of diffeomorphisms of the circle
$D={Diff}_+(S^1)$ and $C^{\infty}(S^{1}, {\bf R})$ functions, classify its
coadjoint orbits and prove the integrability of hamiltonian (Generalized
Dispersive Water Waves (DWW) and KdV-type) systems related to corresponding Lie
algebra centrally extended by Kac-Moody, Virasoro and semidirect product
cocycles with arbitrary coefficients.
|
[
{
"version": "v1",
"created": "Wed, 2 Aug 1995 12:20:24 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Zujewski",
"A.",
""
]
] |
solv-int/9508001
|
Troy Shinbrot
|
Troy Shinbrot (Rutgers University, Piscataway, NJ)
|
Integer spin particles necessarily produce half-integer angular momentum
in a simple complex and periodic Hamiltonian
|
9 pgs, 2 figures
| null | null | null |
solv-int nlin.SI
| null |
Exact wave functions are is derived from an azimuthally periodic a
self-consistent quantum Hamiltonian in 2+1 dimensions using both the
Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for
both relativistic and non-relativistic equations, integer spin wave equations
necessarily produce half-integer angular momentum in this potential. We find
additionally that the higher energy, relativistic, solutions require an
asymptotically free potential, while the lower energy, Schroedinger, solutions
can exist in a potential that grows linearly with r. These are purely
mathematical results, however we speculate on possible physical
interpretations.
|
[
{
"version": "v1",
"created": "Thu, 10 Aug 1995 17:24:03 GMT"
},
{
"version": "v2",
"created": "Wed, 9 Aug 2006 19:58:45 GMT"
}
] | 2009-09-25T00:00:00 |
[
[
"Shinbrot",
"Troy",
"",
"Rutgers University, Piscataway, NJ"
]
] |
solv-int/9508002
|
Evgenii Sklyanin
|
V.B. Kuznetsov (University of Amsterdam) and E.K.Sklyanin (University
of Tokyo)
|
Separation of variables in the $A_2$ type Jack polynomials
|
17 pages, LATEX, macros included, no figures
|
Various aspects of hypergeometric functions (Japanese) (Kyoto,
1994). Surikaisekikenkyusho Kokyuroku No. 919 (1995), 27-43
| null |
UTMS 95-10; UAMS 95-06
|
solv-int math.QA nlin.SI q-alg
| null |
An integral operator $M$ is constructed performing a separation of variables
for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of
$M$ the CS eigenfunctions (Jack polynomials for the root system $A_2$) are
transformed to the factorized form $\phi(y_1)\phi(y_2)$, where $\phi(y)$ is a
trigonometric polynomial of one variable expressed in terms of the ${}_3F_2$
hypergeometric series. The inversion of $M$ produces a new integral
representation for the $A_2$ Jack polynomials.
|
[
{
"version": "v1",
"created": "Mon, 21 Aug 1995 10:14:18 GMT"
}
] | 2015-11-13T00:00:00 |
[
[
"Kuznetsov",
"V. B.",
"",
"University of Amsterdam"
],
[
"Sklyanin",
"E. K.",
"",
"University\n of Tokyo"
]
] |
solv-int/9508003
|
Robert Conte
|
Micheline Musette (Vrije Universiteit Brussel) and Robert Conte (CEA
Saclay)
|
Non-Fuchsian extension to the Painlev\'e test
|
15 pages, no figure, Latex, to appear in Physics Letters A
| null |
10.1016/0375-9601(95)00602-Y
|
SPEC 94/118
|
solv-int nlin.SI
| null |
We consider meromorphic particular solutions of nonlinear ordinary
differential equations and perform a perturbation {\it \`a la} Poincar\'e
making their linearized equation non-Fuchsian at the movable pole and Fuchsian
at infinity. When the nonlinear equation possesses movable logarithms, they are
detected sooner than with the perturbative (Fuchsian) Painlev\'e test.
|
[
{
"version": "v1",
"created": "Mon, 28 Aug 1995 16:01:37 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Musette",
"Micheline",
"",
"Vrije Universiteit Brussel"
],
[
"Conte",
"Robert",
"",
"CEA\n Saclay"
]
] |
solv-int/9508004
|
Tetsu Yajima
|
Tetsu Yajima and Katsuhiro Nishinari
|
Numerical Studies of Localized Structures on an Uneven Bottom in Two
Dimensions
|
14 pages, RevTeX, 7 figures available upon request
| null | null | null |
solv-int nlin.SI
| null |
The Davey-Stewartson (DS) equations with a perturbation term are presented by
taking a fluid system as an example on an uneven bottom. Stability of dromions,
solutions of the DS equations with localized structures, against the
perturbation is investigated numerically. Dromions decay exponentially under an
effect of the perturbation, while they travel stably after the effect
disappears. The decay ratio of dromions is found to have relation to velocities
of dromions. The important role played by the mean flow, which acts as an
external force to the system, is discussed. These results show that dromions
are quite stable as a localized structure in two dimensions, and they are
expected to observed in various physical systems such as fluid or plasma
systems.
|
[
{
"version": "v1",
"created": "Wed, 30 Aug 1995 07:29:25 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Yajima",
"Tetsu",
""
],
[
"Nishinari",
"Katsuhiro",
""
]
] |
solv-int/9508005
|
Ismagil Habibullin
|
I.T. Habibullin
|
Symmetry approach in boundary value problems
|
7 pages, LaTeX
| null |
10.2991/jnmp.1996.3.1-2.16
| null |
solv-int nlin.SI
| null |
The problem of construction of the boundary conditions for nonlinear
equations is considered compatible with their higher symmetries. Boundary
conditions for the sine-Gordon, Jiber-Shabat and KdV equations are discussed.
New examples are found for the Jiber-Shabat equation.
|
[
{
"version": "v1",
"created": "Thu, 31 Aug 1995 07:07:35 GMT"
},
{
"version": "v2",
"created": "Wed, 6 Sep 1995 02:04:35 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Habibullin",
"I. T.",
""
]
] |
solv-int/9509001
|
Vadim B. Kuznetsov
|
Vadim B. Kuznetsov
|
Hidden symmetry of the quantum Calogero-Moser system
|
16 pages, latex, no figures
|
Phys.Lett.A218(1996) 212-222
|
10.1016/0375-9601(96)00421-5
| null |
solv-int hep-th math.QA nlin.SI q-alg
| null |
Hidden symmetry of the quantum Calogero-Moser system with the inverse-square
potential is explicitly demonstrated in algebraic sense. We find the underlying
algebra explaining the super-integrability phenomenon for this system.
Applications to related multi-variable Bessel functions are also discussed.
|
[
{
"version": "v1",
"created": "Mon, 4 Sep 1995 12:23:57 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Kuznetsov",
"Vadim B.",
""
]
] |
solv-int/9509002
|
1081
|
J. F. van Diejen
|
The relativistic Calogero model in an external field
|
10 pages, LaTeX, Submitted to the Proceedings of the 4th Wigner
Symposium, August 5-11, 1995 Guadalajara, Mexico. Third section corrected
| null | null | null |
solv-int hep-th nlin.SI
| null |
Recent results are surveyed regarding the spectrum and eigenfunctions of the
inverse square Calogero model with harmonic confinement and its relativistic
analogue.
|
[
{
"version": "v1",
"created": "Thu, 7 Sep 1995 01:18:25 GMT"
},
{
"version": "v2",
"created": "Wed, 13 Sep 1995 04:56:24 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"van Diejen",
"J. F.",
""
]
] |
solv-int/9509003
|
Craig A. Tracy
|
Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz)
|
Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
|
16 pages, LaTeX file, no figures. Revision has minor changes
|
Commun.Math.Phys. 179 (1996) 667-680
|
10.1007/BF02100102
| null |
solv-int hep-th math-ph math.MP nlin.SI
| null |
We prove that the solution to a pair of nonlinear integral equations arising
in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent
kernel of the linear integral operator with kernel
exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]
|
[
{
"version": "v1",
"created": "Sat, 9 Sep 1995 00:44:13 GMT"
},
{
"version": "v2",
"created": "Sat, 9 Sep 1995 17:12:41 GMT"
},
{
"version": "v3",
"created": "Tue, 12 Sep 1995 20:44:27 GMT"
}
] | 2009-07-11T00:00:00 |
[
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9509004
|
Pgg
|
P.G.Grinevich (Landau Institute for Theoretical Physics, Moscow,
Russia)
|
Nonisospectral symmetries of the KdV equation and the corresponding
symmetries of the Whitham equations
| null | null | null | null |
solv-int nlin.SI
| null |
In our paper we construct a new infinite family of symmetries of the Whitham
equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary
hydrodynamic-type flows these symmetries are nonhomogeneous (i.e. they act
nontrivially at the constant solutions), are nonlocal, explicitly depend upon
space and time coordinates and form a noncommutative algebra, isomorphic to the
algebra of the polynomial vector fields in the complex plane (Virasoro algebra
with the zero central charge).
|
[
{
"version": "v1",
"created": "Wed, 13 Sep 1995 10:18:25 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Moscow,\n Russia"
]
] |
solv-int/9509005
|
Jarmo Hietarinta
|
Yunbo Zeng and Jarmo Hietarinta
|
Classical Poisson structures and r-matrices from constrained flows
|
16 pages in LaTeX
| null |
10.1088/0305-4470/29/16/038
| null |
solv-int math.QA nlin.SI q-alg
| null |
We construct the classical Poisson structure and $r$-matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the $r$-matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.
|
[
{
"version": "v1",
"created": "Thu, 14 Sep 1995 08:49:51 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Zeng",
"Yunbo",
""
],
[
"Hietarinta",
"Jarmo",
""
]
] |
solv-int/9509006
|
Sergei Ya. Startsev
|
S. Ya. Startsev
|
Differential substitutions and symmetries of hyperbolic equations
|
8 pages, AmSTeX
| null | null | null |
solv-int nlin.PS nlin.SI patt-sol
| null |
There are considered differential substitutions of the form $v=P(x,u,u_{x})$
for which there exists a differential operator $H=\sum^{k}_{i=0} \alpha_{i}
D^{i}_{x}$ such that the differential substitution maps the equation
$u_{t}=H[s(x,P,D_{x}(P),...,D^{k}_{x}(P))]$ into an evolution equation for any
function $s$ and any nonnegative integer $k$. All differential substitutions of
the form $v=P(x,u,u_{x})$ known to the author have this property. For example,
the well-known Miura transformation $v=u_{x}-u^{2}$ maps any equation of the
form $$u_{t}=(D^{2}_{x}+2uD_{x}+2u_{x})
[s(x,u_{x}-u^{2},D_{x}(u_{x}-u^{2}),...,D^{k}_{x}(u_{x}-u^{2}))]$$ into the
equation $$v_{t}=(D^{3}_{x}+4vD_{x}+2v_{x})[s(x,v,{{\partial v}\over{\partial x
}},...,{{\partial^{k} v}\over{\partial x^{k}}})].$$ The complete classification
of such differential substitutions is given. An infinite set of the pairwise
nonequivalent differential substitutions with the property mentioned above is
constructed. Moreover, a general result about symmetries and invariant
functions of hyperbolic equations is obtained.
|
[
{
"version": "v1",
"created": "Fri, 15 Sep 1995 04:11:50 GMT"
},
{
"version": "v2",
"created": "Mon, 25 Sep 1995 06:51:48 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Startsev",
"S. Ya.",
""
]
] |
solv-int/9509007
|
Craig A. Tracy
|
Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz)
|
On Orthogonal and Symplectic Matrix Ensembles
|
34 pages. LaTeX file with one figure. To appear in Commun. Math.
Physics
|
Commun.Math.Phys.177:727-754,1996
|
10.1007/BF02099545
| null |
solv-int hep-th math-ph math.MP nlin.SI
| null |
The focus of this paper is on the probability, $E_\beta(0;J)$, that a set $J$
consisting of a finite union of intervals contains no eigenvalues for the
finite $N$ Gaussian Orthogonal ($\beta=1$) and Gaussian Symplectic ($\beta=4$)
Ensembles and their respective scaling limits both in the bulk and at the edge
of the spectrum. We show how these probabilities can be expressed in terms of
quantities arising in the corresponding unitary ($\beta=2$) ensembles. Our most
explicit new results concern the distribution of the largest eigenvalue in each
of these ensembles. In the edge scaling limit we show that these largest
eigenvalue distributions are given in terms of a particular Painlev\'e II
function.
|
[
{
"version": "v1",
"created": "Sun, 17 Sep 1995 16:59:47 GMT"
}
] | 2014-11-18T00:00:00 |
[
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9509008
| null |
J.A. Mulvey (University of Durham)
|
BiHamiltonian Formulations of the Bateman Equation
|
10 pages, LaTeX article, to appear in Phys. Lett. A
| null |
10.1016/0375-9601(95)00709-C
|
DTP/95/51
|
solv-int hep-th nlin.SI
| null |
We discuss a class of evolution equations equivalent to the simplest
Universal Field Equation, the so--called Bateman equation, and show that all of
them possess (at least) biHamiltonian structure. The first few conserved
charges are calculated.
|
[
{
"version": "v1",
"created": "Thu, 21 Sep 1995 13:44:23 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Mulvey",
"J. A.",
"",
"University of Durham"
]
] |
solv-int/9509009
|
Yunbo Zeng
|
Yunbo Zeng
|
The separability and dynamical $r$-matrix for the constrained flows of
Jaulent-Miodek hierarchy
|
12 pages in LaTeX
| null | null | null |
solv-int nlin.SI
| null |
We show here the separability of Hamilton-Jacobi equation for a hierarchy of
integrable Hamiltonian systems obtained from the constrained flows of the
Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian
systems is constructed. The associated $r$-matrices depend not only on the
spectral parameters, but also on the dynamical variables and, for consistency,
have to obey the classical Yang-Baxter equations of dynamical type. Some new
solutions of classical dynamical Yang-Baxter equations are presented. Thus
these integrable systems provide examples both for the dynamical $r$-matrix and
for the separable Hamiltonian system not having a natural Hamiltonian form.
|
[
{
"version": "v1",
"created": "Mon, 25 Sep 1995 13:59:54 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Zeng",
"Yunbo",
""
]
] |
solv-int/9509010
|
Piotr G. Grinevich
|
P.G.Grinevich (Landau Institute for Theoretical Physics, Moscow,
Russia)
|
Nonsingularity of the direct scattering transform for the KP-2 equation
with real exponentially decaying at infinity potential
|
19 pages, LaTeX, 1 picture in PostScript format included in the end
of the paper and 3 style files
| null | null | null |
solv-int nlin.SI
| null |
We study the direct spectral transform for the heat equation, associated with
the KP-2 equation. We show, that for real nonsingular exponentially decaying at
infinity potentials the direct problem is nonsingular for arbitrary large
potentials. Earlier this statement was proved only for potentials, satisfying
the ``small norm'' assumption.
|
[
{
"version": "v1",
"created": "Mon, 25 Sep 1995 21:22:09 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Moscow,\n Russia"
]
] |
solv-int/9509011
|
Sello Dmp
|
S. Sello (Cise-Innovative Technologies, Milan Italy)
|
Nonlinear Behaviour of Time-Stepping Algorithms for Initial Value
Problems
|
uuencoded compressed postscript file, 12 pages paper with included
figures. (source file: 3.1 Mb)
| null | null |
CISE-SMA950919
|
solv-int nlin.SI
| null |
Recent advances in nonlinear dynamical systems theory provide a new insight
into numerical properties of discrete algorithms developed to solve nonlinear
initial value problems. Basic features like accuracy and stability are well
pointed out through diagrams or maps of computed asymptotic solutions in a
suitable parametric space. Applying this methodology to a nonlinear test
equation, we compared some numerical features of the well known second-order
Crank-Nicolson solver with those of a recent proposed version which is
fourth-order accurate. The approach gives some useful indication on the
capabilities of familiar and innovative ODE integrators when applied to
nonlinear problems.
|
[
{
"version": "v1",
"created": "Wed, 27 Sep 1995 13:50:01 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Sello",
"S.",
"",
"Cise-Innovative Technologies, Milan Italy"
]
] |
solv-int/9509012
| null |
O.Ragnisco (Phys. Dept. Univ. Rome III), M.Bruschi (Phys. Dep. Univ.
Rome "La Sapienza")
|
Peakons, R-Matrix and Toda-Lattice
|
12 plain tex pages
| null |
10.1016/0378-4371(95)00438-6
| null |
solv-int nlin.SI
| null |
The integrability of a family of hamiltonian systems, describing in a
particular case the motionof N ``peakons" (special solutions of the so-called
Camassa-Holm equation) is established in the framework of the $r$-matrix
approach, starting from its Lax representation. In the general case, the
$r$-matrix is a dynamical one and has an interesting though complicated
structure. However, for a particular choice of the relevant parameters in the
hamiltonian (the one corresponding to the pure ``peakons" case), the $r$-matrix
becomes essentially constant, and reduces to the one pertaining to the finite
(non-periodic) Toda lattice. Intriguing consequences of such property are
discussed and an integrable time discretisation is derived.
|
[
{
"version": "v1",
"created": "Thu, 28 Sep 1995 14:00:56 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Ragnisco",
"O.",
"",
"Phys. Dept. Univ. Rome III"
],
[
"Bruschi",
"M.",
"",
"Phys. Dep. Univ.\n Rome \"La Sapienza\""
]
] |
solv-int/9510001
|
Peter Nattermann
|
P. Nattermann and R. Zhdanov
|
On Integrable Doebner-Goldin Equations
|
23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.sty
|
J.Phys.A29:2869-2886,1996
|
10.1088/0305-4470/29/11/021
|
ASI-TPA/8/95
|
solv-int hep-th nlin.SI quant-ph
| null |
We suggest a method for integrating sub-families of a family of nonlinear
{\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc
G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie}
symmetries. Since the method of integration involves non-local transformations
of dependent and independent variables, general solutions obtained include
implicitly determined functions. By properly specifying one of the arbitrary
functions contained in these solutions, we obtain broad classes of explicit
square integrable solutions. The physical significance and some analytical
properties of the solutions obtained are briefly discussed.
|
[
{
"version": "v1",
"created": "Tue, 10 Oct 1995 09:46:27 GMT"
}
] | 2008-11-26T00:00:00 |
[
[
"Nattermann",
"P.",
""
],
[
"Zhdanov",
"R.",
""
]
] |
solv-int/9510002
|
Benjamin Enriquez
|
B. Enriquez, A.Yu. Orlov, V.N. Rubtsov
|
Dispersionful analogues of Benney's equations and $N$-wave systems
|
12 pages, latex, no figures
| null |
10.1088/0266-5611/12/3/005
| null |
solv-int hep-th nlin.SI
| null |
We recall Krichever's construction of additional flows to Benney's hierarchy,
attached to poles at finite distance of the Lax operator. Then we construct a
``dispersionful'' analogue of this hierarchy, in which the role of poles at
finite distance is played by Miura fields. We connect this hierarchy with
$N$-wave systems, and prove several facts about the latter (Lax representation,
Chern-Simons-type Lagrangian, connection with Liouville equation,
$\tau$-functions).
|
[
{
"version": "v1",
"created": "Wed, 11 Oct 1995 14:02:59 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Enriquez",
"B.",
""
],
[
"Orlov",
"A. Yu.",
""
],
[
"Rubtsov",
"V. N.",
""
]
] |
solv-int/9510003
|
Leon Jerome
|
J. Leon, (Physique Mathematique et Theorique, Montpellier-France)
|
Solution of SRS on the finite interval
|
Revised version, Submitted to Phys. Lett. A, revtex, NO figure
| null | null | null |
solv-int nlin.SI
| null |
The equations of transient stimulated Raman scattering on the finite interval
are solved by the spectral transform method on the semi-line. As the problem
has a free end, the pump and Stokes output at finite distance can be
constructed as the solution of a linear Cauchy-Green integral equation.
|
[
{
"version": "v1",
"created": "Mon, 16 Oct 1995 08:31:02 GMT"
},
{
"version": "v2",
"created": "Fri, 27 Oct 1995 15:30:04 GMT"
},
{
"version": "v3",
"created": "Thu, 22 Feb 1996 14:59:24 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Leon",
"J.",
""
]
] |
solv-int/9510004
|
Richard Ward
|
R. S. Ward
|
Nontrivial scattering of localized solitons in a (2+1)-dimensional
integrable system
|
9 pages, plainTeX, figure not included To appear in Physics Letters A
| null |
10.1016/0375-9601(95)00782-X
|
DTP95/59
|
solv-int nlin.SI
| null |
One usually expects localized solitons in integrable systems to interact
trivially. There is an integrable (2+1)-dimensional chiral equation which
admits multi-soliton solutions with trivial dynamics. This paper describes how
to generate explicit solutions representing nontrivial soliton interactions: in
particular, a head-on collision of two solitons resulting in $90^\circ$
scattering.
|
[
{
"version": "v1",
"created": "Tue, 17 Oct 1995 16:06:07 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Ward",
"R. S.",
""
]
] |
solv-int/9510005
|
Richard Ward
|
T. Ioannidou and R. S. Ward
|
Conserved quantities for integrable chiral equations in 2+1 dimensions
|
10 pages, plainTeX, to appear in Physics Letters A
| null |
10.1016/0375-9601(95)00781-W
|
DTP95/57
|
solv-int nlin.SI
| null |
The integrable (2+1)-dimensional chiral equations are related to the
self-dual Yang-Mills equation. Previously-known nonlocal conservation laws do
not yield finite conserved charges, because the relevant spatial integrals
diverge. We exhibit infinite sequences of conserved quantities that do exist,
and have a simple explicit form.
|
[
{
"version": "v1",
"created": "Tue, 17 Oct 1995 16:25:58 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Ioannidou",
"T.",
""
],
[
"Ward",
"R. S.",
""
]
] |
solv-int/9510006
|
Saburo Kakei
|
Saburo Kakei
|
Toda Lattice Hierarchy and Zamolodchikov's Conjecture
|
6 pages, LaTeX file, no figures
| null |
10.1143/JPSJ.65.337
| null |
solv-int hep-th nlin.SI
| null |
In this letter, we show that certain Fredholm determinant $D(\lambda;t)$,
introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit
of soliton solution for the Toda lattice hierarchy with 2-periodic reduction
condition.
|
[
{
"version": "v1",
"created": "Mon, 23 Oct 1995 10:14:42 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Kakei",
"Saburo",
""
]
] |
solv-int/9510007
|
Juri Suris
|
Yuri B. Suris (University of Bremen, Germany)
|
A discrete time relativistic Toda lattice
|
32 pages, LaTeX
|
J. Phys. A: Math. and Gen., 1996, V. 29, p. 451-465.
|
10.1088/0305-4470/29/2/022
| null |
solv-int nlin.SI
| null |
Four integrable symplectic maps approximating two Hamiltonian flows from the
relativistic Toda hierarchy are introduced. They are demostrated to belong to
the same hierarchy and to examplify the general scheme for symplectic maps on
groups equiped with quadratic Poisson brackets. The initial value problem for
the difference equations is solved in terms of a factorization problem in a
group. Interpolating Hamiltonian flows are found for all the maps.
|
[
{
"version": "v1",
"created": "Mon, 23 Oct 1995 14:42:07 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Suris",
"Yuri B.",
"",
"University of Bremen, Germany"
]
] |
solv-int/9510008
| null |
Petro Holod and Sergey Kondratiuk
|
The Orbit Method in the Finite Zone Integration Theory
|
12 pages, no figures, LaTeX, a contrubution to the XII Hutsulian
Workshop "Methods of Mathematical Physics", Rakhov, 1995, september 11-17
| null | null | null |
solv-int hep-th nlin.SI
| null |
A construction of integrable hamiltonian systems associated with different
graded realizations of untwisted loop algebras is proposed. Such systems have
the form of Euler - Arnold equations on orbits of loop algebras. The proof of
completeness of the integrals of motion is carried out independently of the
realization of the loop algebra. The hamiltonian systems obtained are shown to
coincide with hierarchies of higher stationary equations for some nonlinear
PDE's integrable by inverse scattering method.
We apply the general scheme for the principal and homogeneous realizations of
the loop algebra $ sl_3(\R)\otimes{\cal P}(\lambda,\lambda^{-1}) $. The
corresponding equations on the degenerated orbit are interpreted as the
Boussinesq's and two-component modified KDV equations respectively. The scalar
Lax representation for the Boussinesq's equation is found in terms of
coordinates on the orbit applying the Drinfeld - Sokolov reduction procedure.
|
[
{
"version": "v1",
"created": "Mon, 23 Oct 1995 13:45:05 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Holod",
"Petro",
""
],
[
"Kondratiuk",
"Sergey",
""
]
] |
solv-int/9510009
|
Henrik Aratyn
|
H. Aratyn, E. Nissimov and S. Pacheva
|
On Integrable Models and their Interrelations
|
LaTeX, 9 pgs, Talk given at the Theoretical Physics Symposium in
honor of Paulo Leal Ferreira (S\~{a}o Paulo, August 7-11,1995)
| null | null |
UICHEP-TH/95-11
|
solv-int nlin.SI
| null |
We present an elementary discussion of the Calogero-Moser model. This gives
us an opportunity to illustrate basic concepts of the dynamical integrable
models. Some ideas are also presented regarding interconnections between
integrable models based on the relation established between the Calogero-Moser
model and the truncated KP hierarchy of Burgers-Hopf type.
|
[
{
"version": "v1",
"created": "Mon, 23 Oct 1995 22:03:23 GMT"
},
{
"version": "v2",
"created": "Mon, 30 Oct 1995 17:21:33 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Aratyn",
"H.",
""
],
[
"Nissimov",
"E.",
""
],
[
"Pacheva",
"S.",
""
]
] |
solv-int/9510010
|
Basile Grammaticos
|
B. Grammaticos and A. Ramani
|
The Gambier Mapping
|
PlainTeX
| null |
10.1016/0378-4371(95)00213-8
| null |
solv-int nlin.SI
| null |
We propose a discrete form for an equation due to Gambier and which belongs
to the class of the fifty second order equations that possess the Painleve
property. In the continuous case, the solutions of the Gambier equation is
obtained through a system of Riccati equations. The same holds true in the
discrete case also. We use the singularity confinement criterion in order to
study the integrability of this new mapping.
|
[
{
"version": "v1",
"created": "Mon, 30 Oct 1995 13:57:59 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Grammaticos",
"B.",
""
],
[
"Ramani",
"A.",
""
]
] |
solv-int/9510011
|
Basile Grammaticos
|
A. Ramani and B. Grammaticos
|
Discrete Painleve equations: coalescences, limits and degeneracies
|
PlainTeX
| null |
10.1016/0378-4371(95)00439-4
| null |
solv-int nlin.SI
| null |
Starting from the standard form of the five discrete Painlev\'e equations we
show how one can obtain (through appropriate limits) a host of new equations
which are also the discrete analogues of the continuous Painlev\'e equations. A
particularly interesting technique is the one based on the assumption that some
simplification takes place in the autonomous form of the mapping following
which the deautonomization leads to a new $n$-dependence and introduces more
new discrete Painlev\'e equations.
|
[
{
"version": "v1",
"created": "Thu, 2 Nov 1995 16:46:04 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Ramani",
"A.",
""
],
[
"Grammaticos",
"B.",
""
]
] |
solv-int/9510012
|
Wen-Xiu Ma
|
Wen-Xiu Ma, Benno Fuchssteiner and Walter Oevel (Paderborn University,
Germany)
|
A three-by-three matrix spectral problem for AKNS hierarchy and its
binary Nonlinearization
|
21pages, in Latex
| null |
10.1016/S0378-4371(96)00225-7
| null |
solv-int hep-th nlin.SI
| null |
A three-by-three matrix spectral problem for AKNS soliton hierarchy is
proposed and the corresponding Bargmann symmetry constraint involved in Lax
pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax
systems possess classical Hamiltonian structures, in which the nonlinearized
spatial system is intimately related to stationary AKNS flows. These
nonlinearized Lax systems also lead to a sort of involutive solutions to each
AKNS soliton equation.
|
[
{
"version": "v1",
"created": "Thu, 2 Nov 1995 22:35:37 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Ma",
"Wen-Xiu",
"",
"Paderborn University,\n Germany"
],
[
"Fuchssteiner",
"Benno",
"",
"Paderborn University,\n Germany"
],
[
"Oevel",
"Walter",
"",
"Paderborn University,\n Germany"
]
] |
solv-int/9511001
|
Atsushi SLIME Nagai
|
Atsushi Nagai and Junkichi Satsuma
|
Discrete soliton equations and convergence acceleration algorithms
|
11 pages, LaTeX file, no figures
| null |
10.1016/0375-9601(95)00865-9
| null |
solv-int nlin.SI
| null |
Some of the well-known convergence acceleration algorithms, when viewed as
two-variable difference equations, are equivalent to discrete soliton
equations. It is shown that the $\eta-$algorithm is nothing but the discrete
KdV equation. In addition, one generalized version of the $\rho-$algorithm is
considered to be integrable discretization of the cylindrical KdV equation.
|
[
{
"version": "v1",
"created": "Tue, 7 Nov 1995 11:31:47 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Nagai",
"Atsushi",
""
],
[
"Satsuma",
"Junkichi",
""
]
] |
solv-int/9511002
|
Garcia Ariel
|
Ariel O. Garcia and Roberto C. Trinchero
|
Constructive building of the Lax pair in the non-linear sigma model
|
10 pages, LaTeX2e and AMSLaTeX, no extra macros, one latex figure
|
J.Math.Phys. 37 (1996) 3973-3981
|
10.1063/1.531610
| null |
solv-int hep-th nlin.SI
| null |
A derivation of the Lax pair for the (1+1)-dimensional non-linear sigma-model
is described. Its main benefit is to have a clearer physical origin and to
allow the study of a generalization to higher dimensions.
|
[
{
"version": "v1",
"created": "Tue, 7 Nov 1995 14:26:03 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Garcia",
"Ariel O.",
""
],
[
"Trinchero",
"Roberto C.",
""
]
] |
solv-int/9511003
|
Helge Frauenkron
|
Alessandro Torcini, Helge Frauenkron, Peter Grassberger (Theoretische
Physik, Bergische Universit\"at-Gesamthochschule Wuppertal, Wuppertal,
Germany)
|
A Novel Integration Scheme for Partial Differential Equations: an
Application to the Complex Ginzburg-Landau Equation
|
10 pages Postscript + 2 figures, uudecoded, gzipped, tarred submitted
to Physica D
| null | null | null |
solv-int nlin.SI
| null |
A new integration scheme, combining the stability and the precision of usual
pseudo-spectral codes with the locality of finite differences methods, is
introduced. It turns out to be particularly suitable for the study of front and
disturbance propagation in extended systems. An application to the complex
Ginzburg-Landau equation shows the higher precision of this method with respect
to spectral ones.
|
[
{
"version": "v1",
"created": "Thu, 9 Nov 1995 15:58:58 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Torcini",
"Alessandro",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
],
[
"Frauenkron",
"Helge",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
],
[
"Grassberger",
"Peter",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
]
] |
solv-int/9511004
|
Latypov A. M.
|
Azat M. Latypov
|
Approximate Lie Group Analysis of Finite-difference Equations
|
21 pages, LaTeX
| null | null | null |
solv-int nlin.SI
| null |
Approximate group analysis technique, that is, the technique combining the
methodology of group analysis and theory of small perturbations, is applied to
finite-difference equations approximating ordinary differential equations.
Finite-difference equations are viewed as a system of algebraic equations with
a small parameter, introduced through the definitions of finite-difference
derivatives. It is shown that application of the approximate invariance
criterion to this algebraic system results in relations that can be viewed as
prolongation formulae and the invariance criterion for the differential
approximation of these finite-difference equations. This allows us to study the
group properties of the finite-difference equations by analyzing the group
properties of their differential approximations, which are the differential
equations with a small parameter. In particular, the question of whether the
group, admitted by the original differential equation, can be corrected by
adding the first-order perturbation to it, so that the resulting group with a
small parameter is approximately admitted by the finite-difference
approximation, is studied. It is shown by examples that, for a given
differential equation, its finite--difference approximation and the group, such
a correction may not always be possible. It is also demonstrated that the
finite--difference approximation can be modified in such a way that the
correction becomes possible.
|
[
{
"version": "v1",
"created": "Thu, 9 Nov 1995 21:12:09 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Latypov",
"Azat M.",
""
]
] |
solv-int/9511005
|
Wen-Xiu Ma
|
Wen-Xiu Ma, Benno Fuchssteiner
|
Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov
Equation
|
14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the
original latex file is not complete
| null |
10.1016/0020-7462(95)00064-X
| null |
solv-int nlin.SI
| null |
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov
equation are presented through two ans\"atze. By a Cole-Hopf transformation,
this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear
equation and further two solutions to describe nonlinear interaction of
traveling waves are generated. B\"acklund transformations of the linear form
and some special cases are considered.
|
[
{
"version": "v1",
"created": "Tue, 14 Nov 1995 16:41:05 GMT"
},
{
"version": "v2",
"created": "Thu, 30 Nov 1995 18:01:48 GMT"
},
{
"version": "v3",
"created": "Fri, 1 Dec 1995 14:21:48 GMT"
}
] | 2019-08-15T00:00:00 |
[
[
"Ma",
"Wen-Xiu",
""
],
[
"Fuchssteiner",
"Benno",
""
]
] |
solv-int/9511006
|
Ravil I. Yamilov
|
D. Levi, R. Yamilov
|
Classification of evolutionary equations on the lattice. I. The general
theory
|
24 pages, AmsTeX
| null | null | null |
solv-int nlin.SI
| null |
A modification of the symmetry approach for the classification of integrable
differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n,
u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the
well-known Volterra and Toda equations can be written in this form). If before,
in the framework of the symmetry approach, only equations similar to $$ u_{n,t}
= f(u_{n-1}, u_n, u_{n+1}), $$ i.e. defined by a function $f$, were considered,
now we have an infinite set $f_n$ of a priori quite different functions.
|
[
{
"version": "v1",
"created": "Thu, 16 Nov 1995 09:58:04 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Levi",
"D.",
""
],
[
"Yamilov",
"R.",
""
]
] |
solv-int/9511007
|
Ayrton Zadra
|
L.E. Saltini and A. Zadra
|
Algebra of Non-Local Charges in Supersymmetric Non-Linear Sigma Models
|
LateX file, 19 pages, figures included with epsf; file with figures
has been replaced
|
Int.J.Mod.Phys. A12 (1997) 419-436
|
10.1142/S0217751X97000487
|
IFUSP/P-1188
|
solv-int hep-th nlin.SI
| null |
We propose a graphic method to derive the classical algebra (Dirac brackets)
of non-local conserved charges in the two dimensional supersymmetric non-linear
$O(N)$ sigma model. As in the purely bosonic theory we find a cubic Yangian
algebra. We also consider the extension of graphic methods to other integrable
theories.
|
[
{
"version": "v1",
"created": "Thu, 16 Nov 1995 19:21:32 GMT"
},
{
"version": "v2",
"created": "Fri, 17 Nov 1995 13:04:09 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Saltini",
"L. E.",
""
],
[
"Zadra",
"A.",
""
]
] |
solv-int/9511008
| null |
E. Alfinito, G. Profilo, G. Soliani
|
Properties of equations of the continuous Toda type
|
LaTex file, 27 pages
|
J.Phys.A30:1527-1547,1997
|
10.1088/0305-4470/30/5/019
| null |
solv-int gr-qc hep-th nlin.SI
| null |
We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter $\ep$. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for $\ep =0$ and $\ep \ne 0$, whose
properties arising in the above frameworks are mutually compared. For $\ep =0$,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group $E_{2}$, a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For $\ep\,\ne\,0,$ we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.
|
[
{
"version": "v1",
"created": "Thu, 23 Nov 1995 10:21:29 GMT"
}
] | 2016-09-08T00:00:00 |
[
[
"Alfinito",
"E.",
""
],
[
"Profilo",
"G.",
""
],
[
"Soliani",
"G.",
""
]
] |
solv-int/9511009
|
Robert Carroll
|
Robert Carroll (Mathematics Department, University of Illinois,
Urbana, IL)
|
Remarks on the Whitham equations
|
Latex, 81 pages, run three times for table of contents
| null | null | null |
solv-int hep-th nlin.SI
| null |
We survey some topics involving the Whitham equations, concentrating on the
role of the product of the wave function and its adjoint in averaging and in
producing Cauchy kernels and differentials on Riemann surfaces. There are also
some new results.
|
[
{
"version": "v1",
"created": "Fri, 24 Nov 1995 13:28:44 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Carroll",
"Robert",
"",
"Mathematics Department, University of Illinois,\n Urbana, IL"
]
] |
solv-int/9512001
|
Juri Suris
|
Yuri B. Suris (University of Bremen, Germany)
|
A discrete time peakons lattice
|
14 pages, LaTeX
|
Phys. Lett. A217, 1996, p. 321-329.
|
10.1016/0375-9601(96)00375-1
| null |
solv-int nlin.SI
| null |
A discretization of the peakons lattice is introduced, belonging to the same
hierarchy as the continuous--time system. The construction examplifies the
general scheme for integrable discretization of systems on Lie algebras with
$r$--matrix Poisson brackets. An initial value problem for the difference
equations is solved in terms of a factorization problem in a group.
Interpolating Hamiltonian flow is found. A variational (Lagrangian) formulation
is also given.
|
[
{
"version": "v1",
"created": "Fri, 1 Dec 1995 11:48:54 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Suris",
"Yuri B.",
"",
"University of Bremen, Germany"
]
] |
solv-int/9512002
|
Wen-Xiu Ma
|
Wen-Xiu Ma
|
Binary nonlinearization for the Dirac systems
|
11 pages, plaintex(vanilla.sty), to appear in Chinese Ann. of Math. B
| null | null | null |
solv-int nlin.SI
| null |
A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint
Lax pairs of the Dirac systems. It is shown that the spatial part of the
nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville
integrable Hamiltonian system and that under the control of the spatial part,
the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are
interpreted as a hierarchy of commutative, finite dimensional Liouville
integrable Hamiltonian systems whose Hamiltonian functions consist of a series
of integrals of motion for the spatial part. Moreover an involutive
representation of solutions of the Dirac systems exhibits their integrability
by quadratures. This kind of symmetry constraint procedure involving the
spectral problem and the adjoint spectral problem is referred to as a binary
nonlinearization technique like a binary Darboux transformation.
|
[
{
"version": "v1",
"created": "Wed, 6 Dec 1995 16:58:48 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Ma",
"Wen-Xiu",
""
]
] |
solv-int/9512003
|
Gennady El
|
G.A. El
|
On evolution of multiphase nonlinear modulated waves
|
15 pages of Standard LaTeX and 4 figures. The figures are available
by fax. Please send your request by e-mail address: [email protected]
| null | null | null |
solv-int nlin.SI
| null |
We present a fundamental solution to an initial value problem for the
KdV-Whitham system in an explicit integral form. Monotonically decreasing
initial data with finite number of breaking points are considered. Generating
function for the commuting flows of the averaged KdV hieararchy producing the
analytical solutions to the KdV-Whitham system is constructed.
|
[
{
"version": "v1",
"created": "Wed, 6 Dec 1995 15:35:55 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"El",
"G. A.",
""
]
] |
solv-int/9512004
|
Daniel Finley
|
J. D. Finley, III (University of New Mexico)
|
Estabrook-Wahlquist Prolongations and Infinite-Dimensional Algebras
|
10 pages, plain TeX-file, to be published in proceedings of the VIIth
International Conference on Symmetry Methods in Physics, held at Dubna,
Russia, in July, 1995
| null | null | null |
solv-int nlin.SI
| null |
Detailed mappings between zero-curvture equations for prolongation structures
of nonlinear pde's and Estabrook-Wahlquist algorithms for same are given. The
differences are exemplified by studies of the sine-Gordon equation. An example
where the prolongation structure must be infinite-dimensional is given by the
Robinson-Trautman equation, where the minimal algebra is $K_2$. In general
these algorithms require integration of vector-field valued pde's; solutions of
simultaneous flow equations are given. Applications to coupled systems of flow
equations are given, where the result describes Lie algebras of vector fields
vertical over fibers of pseudopotentials over a jet bundle appropriate for a
given system of pde's; algebras invariant under sl(2,C) are of special
interest.
|
[
{
"version": "v1",
"created": "Fri, 8 Dec 1995 19:47:08 GMT"
}
] | 2012-08-27T00:00:00 |
[
[
"Finley",
"J. D.",
"",
"University of New Mexico"
],
[
"III",
"",
"",
"University of New Mexico"
]
] |
solv-int/9512005
|
Rinat Kashaev
|
R.M. Kashaev
|
On Discrete 3-Dimensional Equations Associated with the Local
Yang-Baxter Relation
|
10 pages, LaTeX, no figures
| null |
10.1007/BF01815521
|
ENSLAPP-L-569/95
|
solv-int nlin.SI
| null |
The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a
proper generalization to 3 dimensions of the zero curvature relation. Recently,
Korepanov has constructed an infinite set of integrable 3-dimensional lattice
models, and has related them to solutions to the local YBE. The simplest
Korepanov's model is related to the star-triangle relation in the Ising model.
In this paper the corresponding discrete equation is derived. In the continuous
limit it leads to a differential 3d equation, which is symmetric with respect
to all permutations of the three coordinates. A similar analysis of the
star-triangle transformation in electric networks leads to the discrete
bilinear equation of Miwa, associated with the BKP hierarchy. Some related
operator solutions to the tetrahedron equation are also constructed.
|
[
{
"version": "v1",
"created": "Mon, 11 Dec 1995 18:24:13 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Kashaev",
"R. M.",
""
]
] |
solv-int/9512006
|
Costas Efthimiou
|
S. A. Apikyan and C. J. Efthimiou
|
Integrable Models of the CFT on Hyper-Elliptic Surfaces
|
Postscript file available at
http://www.tau.ac.il/~costas/papers/HES-2.ps; revised version to appear in
Phys. Lett. B
|
Phys.Lett. B383 (1996) 397-402
|
10.1016/0370-2693(96)00666-1
|
Tel Aviv University Preprint TAUP 2308-95
|
solv-int hep-th nlin.SI
| null |
In this letter, we continue the work we started at a previous paper and we
propose new series of integrable models in quantum field theory. These models
are obtained as perturbed models of the minimal conformal field theories on the
hyper-elliptic surfaces by particular relevant operators of the untwisted
sector. The quantum group symmetry of the models is also discussed.
|
[
{
"version": "v1",
"created": "Tue, 12 Dec 1995 14:31:03 GMT"
},
{
"version": "v2",
"created": "Wed, 22 May 1996 13:49:40 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Apikyan",
"S. A.",
""
],
[
"Efthimiou",
"C. J.",
""
]
] |
solv-int/9512007
|
Juri Suris
|
Yu.B.Suris (University of Bremen, Germany)
|
Discrete time Bogoyavlensky lattices
|
22 pages, LaTeX, revised version (the third lattice discretized now!)
|
J. Math. Phys., 1996, V. 37, p. 3982-3996.
|
10.1063/1.531611
| null |
solv-int nlin.SI
| null |
Discretizations of the Bogoyavlensky lattices are introduced, belonging to
the same hierarchies as the continuous--time systems. The construction
exemplifies the general scheme for integrable discretization of systems on Lie
algebras with $r$--matrix Poisson brackets. An initial value problem for the
difference equations is solved in terms of a factorization problem in a group.
Interpolating Hamiltonian flow is found.
|
[
{
"version": "v1",
"created": "Wed, 20 Dec 1995 17:03:15 GMT"
},
{
"version": "v2",
"created": "Tue, 2 Jan 1996 17:27:17 GMT"
}
] | 2009-10-28T00:00:00 |
[
[
"Suris",
"Yu. B.",
"",
"University of Bremen, Germany"
]
] |
solv-int/9512008
|
Henrik Aratyn
|
H. Aratyn, E. Nissimov and S. Pacheva
|
Constrained KP Hierarchies: Darboux-B\"acklund Solutions and Additional
Symmetries
|
LaTeX, 15 pgs, To be published in Proceedings of the second Summer
Workshop, Razlog/Bulgaria, Aug-Sept 1995
| null | null |
INRNE-TH/95-15, UICHEP-TH/95-14
|
solv-int hep-th nlin.SI
| null |
We illustrate the basic notions of {\em additional non-isospectral
symmetries} and their interplay with the discrete {\em \DB transformations} of
integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili}
(\cKP) integrable hierarchies. As a main application we present the solution of
discrete multi-matrix string models in terms of Wronskian $\t$-functions of
graded $SL(m,1)$ \cKP hierarchies.
|
[
{
"version": "v1",
"created": "Thu, 28 Dec 1995 15:23:26 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Aratyn",
"H.",
""
],
[
"Nissimov",
"E.",
""
],
[
"Pacheva",
"S.",
""
]
] |
solv-int/9601001
|
Jose Carlos Brunelli P.
|
J. C. Brunelli
|
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
|
16 pages, plain TeX
|
Rev.Math.Phys. 8 (1996) 1041-1054
|
10.1142/S0129055X96000378
| null |
solv-int hep-th nlin.SI
| null |
We study from a Hamiltonian point of view the generalized dispersionless KdV
hierarchy of equations. From the so called dispersionless Lax representation of
these equations we obtain three compatible Hamiltonian structures. The second
and third Hamiltonian structures are calculated directly from the r-matrix
approach. Since the third structure is not related recursively with the first
two ones the generalized dispersionless KdV hierarchy can be characterized as a
truly tri-Hamiltonian system.
|
[
{
"version": "v1",
"created": "Fri, 5 Jan 1996 16:37:32 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Brunelli",
"J. C.",
""
]
] |
solv-int/9601002
|
Manuel Manas
|
F. Guil, M. Ma\~nas
|
The Three-Wave Resonant Interaction: Deformation of the Plane-Wave
Solutions and Darboux Transformations
|
16 pages, AMSLaTeX
| null | null | null |
solv-int nlin.SI
| null |
The plane wave solutions of the three-wave resonant interaction in the plane
are considered. It is shown that rank-one constraints over the right
derivatives of invertible operators on an arbitrary linear space gives
solutions of the three-wave resonant interaction that can be understood as a
Darboux transformation of the plane wave solutions. The method is extended
further to obtain general Darboux transformations: for any solution of the
three-wave interaction problem and vector solutions of the corresponding Lax
pair large families of new solutions, expressed in terms of Grammian type
determinants of these vector solutions, are given.
|
[
{
"version": "v1",
"created": "Thu, 11 Jan 1996 15:03:32 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Guil",
"F.",
""
],
[
"Mañas",
"M.",
""
]
] |
solv-int/9601003
|
Wen-Xiu Ma
|
Wen-Xiu Ma and Benno Fuchssteiner (University of Paderborn)
|
The Bi-Hamiltonian Structure of the Perturbation Equations of KdV
Hierarchy
|
9 pages, Latex, submitted to Phys. Lett. A
| null |
10.1016/0375-9601(96)00112-0
| null |
solv-int nlin.SI
| null |
The bi-Hamiltonian structure is established for the perturbation equations of
KdV hierarchy and thus the perturbation equations themselves provide also
examples among typical soliton equations. Besides, a more general
bi-Hamiltonian integrable hierarchy is proposed and a remark is given for a
generalization of the resulting perturbation equations to $1+2$ dimensions.
|
[
{
"version": "v1",
"created": "Fri, 26 Jan 1996 12:13:05 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Ma",
"Wen-Xiu",
"",
"University of Paderborn"
],
[
"Fuchssteiner",
"Benno",
"",
"University of Paderborn"
]
] |
solv-int/9601004
|
Michio Jimbo
|
M. Jimbo, H. Sakai, A. Ramani and B. Grammaticos
|
Bilinear structure and Schlesinger transforms of the $q$-P$_{\rm III}$
and $q$-P$_{\rm VI}$ equations
|
10 pages, Plain TeX
| null |
10.1016/0375-9601(96)00336-2
| null |
solv-int nlin.SI
| null |
We show that the recently derived ($q$-) discrete form of the Painlev\'e VI
equation can be related to the discrete P$_{\rm III}$, in particular if one
uses the full freedom in the implementation of the singularity confinement
criterion. This observation is used here in order to derive the bilinear forms
and the Schlesinger transformations of both $q$-P$_{\rm III}$ and $q$-P$_{\rm
VI}$.
|
[
{
"version": "v1",
"created": "Sat, 27 Jan 1996 00:32:01 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Jimbo",
"M.",
""
],
[
"Sakai",
"H.",
""
],
[
"Ramani",
"A.",
""
],
[
"Grammaticos",
"B.",
""
]
] |
solv-int/9601005
|
Leon Jerome
|
M. Boiti, J. Leon, F. Pempinelli, (Physique Mathematique et Theorique,
CNRS, F-34095 MONTPELLIER)
|
Nonlinear Discrete Systems with Nonanalytic Dispersion Relations
|
RevTex file, to appear in Journ. Math. Phys
| null |
10.1063/1.531542
| null |
solv-int nlin.SI
| null |
A discrete system of coupled waves (with nonanalytic dispersion relation) is
derived in the context of the spectral transform theory for the Ablowitz Ladik
spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave
evolution problem is a discrete version of the stimulated Raman scattering
equations, and it is shown to be solvable for arbitrary boundary value of the
two radiation fields and initial value of the medium state. The spectral
transform is constructed on the basis of the D-bar approach.
|
[
{
"version": "v1",
"created": "Wed, 31 Jan 1996 15:49:58 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Boiti",
"M.",
""
],
[
"Leon",
"J.",
""
],
[
"Pempinelli",
"F.",
""
]
] |
solv-int/9601006
|
Ron Perline
|
Ron Perline (Drexel University)
|
Localized Induction Hierarchy and Weingarten Systems
|
AMSTeX file (10 pages) with one Postscript graphic; submitted to
Physics Letters A
| null |
10.1016/0375-9601(96)00513-0
| null |
solv-int nlin.SI
| null |
We describe a method of constructing Weingarten systems of triply orthogonal
coordinates, related to the localized induction equation hierarchy of
integrable geometric evolution equations
|
[
{
"version": "v1",
"created": "Thu, 1 Feb 1996 19:27:18 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Perline",
"Ron",
"",
"Drexel University"
]
] |
solv-int/9602001
|
Harold Widom
|
Harold Widom (University of California, Santa Cruz)
|
Some Classes of Solutions to the Toda Lattice Hierarchy
|
LaTeX file, 18 pages. Results generalized and applications to the
Toda equations added
|
Commun.Math.Phys. 184 (1997) 653-667
|
10.1007/s002200050078
| null |
solv-int hep-th math.FA nlin.SI
| null |
We apply an analogue of the Zakharov-Shabat dressing method to obtain
infinite matrix solutions to the Toda lattice hierarchy. Using an operator
transformation we convert some of these into solutions in terms of integral
operators and Fredholm determinants. Others are converted into a class of
operator solutions to the $l$-periodic Toda hierarchy.
|
[
{
"version": "v1",
"created": "Thu, 8 Feb 1996 22:50:20 GMT"
},
{
"version": "v2",
"created": "Fri, 8 Mar 1996 21:26:59 GMT"
},
{
"version": "v3",
"created": "Wed, 2 Oct 1996 18:06:11 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Widom",
"Harold",
"",
"University of California, Santa Cruz"
]
] |
solv-int/9602002
|
J. C. de Gier
|
Jan de Gier, Bernard Nienhuis (University of Amsterdam)
|
Exact Solution of an Octagonal Random Tiling Model
|
4 pages,3 Postscript figures, uses revtex
|
Phys. Rev. Lett. 76 (1996) 2918-2921
|
10.1103/PhysRevLett.76.2918
|
ITFA 95-24
|
solv-int cond-mat hep-th nlin.SI
| null |
We consider the two-dimensional random tiling model introduced by Cockayne,
i.e. the ensemble of all possible coverings of the plane without gaps or
overlaps with squares and various hexagons. At the appropriate relative
densities the correlations have eight-fold rotational symmetry. We reformulate
the model in terms of a random tiling ensemble with identical rectangles and
isosceles triangles. The partition function of this model can be calculated by
diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations
can be solved providing {\em exact} values of the entropy and elastic
constants.
|
[
{
"version": "v1",
"created": "Fri, 23 Feb 1996 09:48:42 GMT"
}
] | 2011-11-29T00:00:00 |
[
[
"de Gier",
"Jan",
"",
"University of Amsterdam"
],
[
"Nienhuis",
"Bernard",
"",
"University of Amsterdam"
]
] |
solv-int/9603001
|
John Harnad
|
M.R. Adams, J. Harnad, and J. Hurtubise
|
Darboux Coordinates on Coadjoint Orbits of Lie Algebras
|
AMSTeX 16pgs
|
Lett.Math.Phys. 40 (1997) 41-57
| null |
CRM 2338 (1996)
|
solv-int hep-th nlin.SI
| null |
The method of constructing spectral Darboux coordinates on finite dimensional
coadjoint orbits in duals of loop algebras is applied to the one pole case,
where the orbit is identified with a coadjoint orbit in the dual of a finite
dimensional Lie algebra. The constructions are carried out explicitly when the
Lie algebra is $\frak{sl}(2,\bold R),\ \frak{sl}(3, \bold R),$ and
$\frak{so}(3, \bold R)$, and for rank two orbits in $\frak{so}(n, \bold R)$. A
new feature that appears is the possibility of identifying spectral Darboux
coordinates associated to ``dynamical" choices of sections of the associated
eigenvector line bundles; i.e. sections that depend on the point within the
given orbit.
|
[
{
"version": "v1",
"created": "Tue, 5 Mar 1996 20:56:47 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Adams",
"M. R.",
""
],
[
"Harnad",
"J.",
""
],
[
"Hurtubise",
"J.",
""
]
] |
solv-int/9603002
|
Basile Grammaticos
|
Y. Ohta, A. Ramani, B. Grammaticos and K.M. Tamizhmani
|
From Discrete to Continuous Painlev\'e Equations: A Bilinear Approach
|
9 pages, plainTeX
| null |
10.1016/0375-9601(96)00292-7
| null |
solv-int nlin.SI
| null |
We present the bilinear forms of the (continuous) Painlev\'e equations
obtained from the continuous limit of the analogous expresssions for the
discrete ones. The advantage of this method is that it leads to very
symmetrical results. A new and interesting result is the bilinearization of the
P$_{\rm VI}$ equation, something that was missing till now.
|
[
{
"version": "v1",
"created": "Fri, 8 Mar 1996 20:01:25 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Ohta",
"Y.",
""
],
[
"Ramani",
"A.",
""
],
[
"Grammaticos",
"B.",
""
],
[
"Tamizhmani",
"K. M.",
""
]
] |
solv-int/9603003
|
Basile Grammaticos
|
B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi and K.M. Tamizhmani
|
Cellular Automata and Ultra-Discrete Painlev\'e Equations
|
8 pages, plainTeX, 2 figures
| null |
10.1016/S0375-9601(96)00934-6
| null |
solv-int nlin.SI
| null |
Starting from integrable cellular automata we present a novel form of
Painlev\'e equations. These equations are discrete in both the independent
variable and the dependent one. We show that they capture the essence of the
behavior of the Painlev\'e equations organizing themselves into a coalescence
cascade and possessing special solutions. A necessary condition for the
integrability of cellular automata is also presented.
|
[
{
"version": "v1",
"created": "Fri, 8 Mar 1996 20:13:30 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Grammaticos",
"B.",
""
],
[
"Ohta",
"Y.",
""
],
[
"Ramani",
"A.",
""
],
[
"Takahashi",
"D.",
""
],
[
"Tamizhmani",
"K. M.",
""
]
] |
solv-int/9603004
|
V. Z. Enolskii
|
Victor Enolskii (Institute of Magnetism, Kiev ) and Mario Salerno
(University of Salerno )
|
Lax representation for two--particle dynamics splitting on two tori
|
9 pages, LaTeX
| null |
10.1088/0305-4470/29/17/002
| null |
solv-int nlin.SI
| null |
Lax representation in terms of $2\times 2$ matrices is constructed for a
separable multiply--periodic system splitting on two tori. Hyperelliptic
Kleinian functions and their reduction to elliptic functions are used.
|
[
{
"version": "v1",
"created": "Tue, 12 Mar 1996 14:47:10 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Enolskii",
"Victor",
"",
"Institute of Magnetism, Kiev"
],
[
"Salerno",
"Mario",
"",
"University of Salerno"
]
] |
solv-int/9603005
|
V. Z. Enolskii
|
Victor Buchstaber (Research Institute of Physico-Technical and
Radio-Technical Measurements, VNIIFTRI, Mendeleevo), Victor Enolskii and
Dmitri Leykin (NASU Institute of Magnetism, Kiev )
|
Hyperelliptic Kleinian functions and applications
|
24 pages, AMSLaTeX2e
| null | null | null |
solv-int nlin.SI
| null |
We develop the theory of hyperelliptic Kleinian functions. As applications we
consider construction of the explicit matrix realization of the hyperelliptic
Kummer varieties, differential operators to have the hyperelliptic curve as
spectral variety, solution of the KdV equations by Kleinian functions.
|
[
{
"version": "v1",
"created": "Sat, 16 Mar 1996 15:27:57 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Buchstaber",
"Victor",
"",
"Research Institute of Physico-Technical and\n Radio-Technical Measurements, VNIIFTRI, Mendeleevo"
],
[
"Enolskii",
"Victor",
"",
"NASU Institute of Magnetism, Kiev"
],
[
"Leykin",
"Dmitri",
"",
"NASU Institute of Magnetism, Kiev"
]
] |
solv-int/9603006
|
V. Kuznetsov
|
F.W. Nijhoff, V.B. Kuznetsov, E.K. Sklyanin and O. Ragnisco
|
Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
|
14 pages, LaTex, equations.sty, no figures, comment on explicit
non-relativistic limit is added
|
J.Phys. A29 (1996) L333-L340
|
10.1088/0305-4470/29/13/005
|
University of Leeds, March 1996
|
solv-int hep-th math.QA nlin.SI q-alg
| null |
The classical r-matrix structure for the generic elliptic
Ruijsenaars-Schneider model is presented. It makes the integrability of this
model as well as of its discrete-time version that was constructed in a recent
paper manifest.
|
[
{
"version": "v1",
"created": "Thu, 21 Mar 1996 11:47:07 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Nijhoff",
"F. W.",
""
],
[
"Kuznetsov",
"V. B.",
""
],
[
"Sklyanin",
"E. K.",
""
],
[
"Ragnisco",
"O.",
""
]
] |
solv-int/9603007
| null |
Mario Salerno (Department of Theoretical Physics, University of
Salerno, Salerno, Italy)
|
The Hubbard model on a complete graph: Exact Analytical results
|
Email:[email protected]
|
Z. Phys. B 99 (1996) 469
|
10.1007/s002570050064
| null |
solv-int cond-mat nlin.SI
| null |
We derive the analytical expression of the ground state of the Hubbard model
with unconstrained hopping at half filling and for arbitrary lattice sites.
|
[
{
"version": "v1",
"created": "Wed, 27 Mar 1996 15:23:55 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Salerno",
"Mario",
"",
"Department of Theoretical Physics, University of\n Salerno, Salerno, Italy"
]
] |
solv-int/9603008
| null |
Mario Salerno (Department of Theoretical Physics, University of
Salerno)
|
Ferromagnetic ground states of the Hubbard model on a complete graph
|
latex file
|
Z. Phys. B 101 (1996) 619
|
10.1007/s002570050254
| null |
solv-int cond-mat nlin.SI
| null |
We use group theory to derive the exact analytical expression of the
ferromagnetic ground states of the Hubbard model on a complete graph for
arbitrary lattice sites f and for arbitrary fillings $N$. We find that for
$t>0$ and for $N=f+1$ the ground state is maximally ferromagnetic with total
spin $S=(f-1)/2$. For $N > f+1$ the ground state is still ferromagnetic but
becomes degenerate with respect to $S$.
|
[
{
"version": "v1",
"created": "Wed, 27 Mar 1996 15:24:15 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Salerno",
"Mario",
"",
"Department of Theoretical Physics, University of\n Salerno"
]
] |
solv-int/9603009
| null |
Mario Salerno (Department of Theoretical Physics, University of
Salerno, Salerno, Italy)
|
SO(4) invariant basis functions for strongly correlated Fermi systems
|
Phys. Lett. A 217(1996)269
|
10.1016/0375-9601(96)00338-6
| null |
solv-int cond-mat nlin.SI
| null |
We show how to construct SO(4) invariant functions for strongly correlated
Fermi systems on lattices of finite sizes. We illustrate the method on the case
of the 1D Hubbard chain with four and with six sites.
|
[
{
"version": "v1",
"created": "Wed, 27 Mar 1996 15:24:35 GMT"
},
{
"version": "v2",
"created": "Fri, 29 Mar 1996 21:10:26 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Salerno",
"Mario",
"",
"Department of Theoretical Physics, University of\n Salerno, Salerno, Italy"
]
] |
|
solv-int/9603010
|
Benzion Shklyar
|
B. Shklyar (Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel)
|
Approximate Controlability by Control Constraints for Infinite
Dimensional Systems
|
12 pages, LaTeX
| null | null |
bimacs-96
|
solv-int nlin.SI
| null |
For linear infinite systems the approximate controllability problem by
control constraints is considered. Controllability conditions represented via
system parameters are obtained. Partial differential control systems and
control systems with delays are considered as an example.
|
[
{
"version": "v1",
"created": "Mon, 1 Apr 1996 14:22:48 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Shklyar",
"B.",
"",
"Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel"
]
] |
solv-int/9603011
| null |
Yuri B. Suris (University of Bremen)
|
Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are
governed by the same r-matrix
| null |
Phys. Lett. A225, 1997, p. 253-262.
|
10.1016/S0375-9601(96)00897-3
| null |
solv-int nlin.SI
| null |
We demonstrate that in a certain gauge the elliptic Ruijsenaars--Schneider
models admit Lax representation governed by the same dynamical $r$--matrix as
their non--relativistic counterparts (Calogero--Moser models). This phenomenon
was previously observed for the rational and hyperbolic models.
|
[
{
"version": "v1",
"created": "Mon, 1 Apr 1996 17:53:45 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Suris",
"Yuri B.",
"",
"University of Bremen"
]
] |
solv-int/9603012
|
Ken Umeno
|
Ken Umeno (Brain Information Processing Group of RIKEN)
|
Non-perturbative non-integrability of non-homogeneous nonlinear lattices
induced by non-resonance hypothesis
|
Latex, 21 pages, to appear in Physica D (1996), ps.Z file available
at http://www.bip.riken.go.jp/irl/chaosken/reulam.ps.Z
|
Physica D94(1996)116-134.
|
10.1016/0167-2789(96)88314-X
| null |
solv-int nlin.SI
| null |
We prove the non-integrability (non-existence of additional analytic
conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU)
lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method
about the variational equations. The key to this analysis is that the normal
variational equations along a certain solution happen to be in a type of Lam\'e
equations. We also introduce the classification problem towards non-homogeneous
nonlinear lattices including FPU lattices using non-integrability preserving
transformation.
|
[
{
"version": "v1",
"created": "Tue, 2 Apr 1996 07:29:09 GMT"
}
] | 2015-06-26T00:00:00 |
[
[
"Umeno",
"Ken",
"",
"Brain Information Processing Group of RIKEN"
]
] |
solv-int/9604001
|
Hsien-chung Kao
|
Hsien-chung Kao, Shih-Chang Lee, and Wen-Jer Tzeng
|
Farey Tree and the Frenkel-Kontorova Model
|
9 pages, uses Revtex.
| null |
10.1103/PhysRevE.55.2628
| null |
solv-int cond-mat nlin.SI
| null |
We solved the Frenkel-Kontorova model with the potential $V(u)= -\frac{1}{2}
|\lambda|(u-{\rm Int}[u]-\frac{1}{2})^2$ exactly. For given $|\lambda|$, there
exists a positive integer $q_c$ such that for almost all values of the tensile
force $\sigma$, the winding number $\omega$ of the ground state configuration
is a rational number in the $q_c$-th level Farey tree. For fixed $\omega=p/q$,
there is a critical $\lambda_c$ when a first order phase transition occurs.
This phase transition can be understood as the dissociation of a large molecule
into two smaller ones in a manner dictated by the Farey tree. A kind of
``commensurate-incommensurate'' transition occurs at critical values of
$\sigma$ when two sizes of molecules co-exist. ``Soliton'' in the usual sense
does not exist but induces a transformation of one size of molecules into the
other.
|
[
{
"version": "v1",
"created": "Tue, 16 Apr 1996 13:54:03 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Kao",
"Hsien-chung",
""
],
[
"Lee",
"Shih-Chang",
""
],
[
"Tzeng",
"Wen-Jer",
""
]
] |
solv-int/9604002
|
A. M. Carroll
|
Daniel Stubbs (University of Western Ontario)
|
Analytic Structure of the Landau-Ginzburg Equation in 2+1 Dimensions
|
6 pages, LaTeX, submitted to the Journal of Mathematical Physics
| null | null | null |
solv-int nlin.SI
| null |
In this paper, two methods are employed to investigate for which values of
the parameters, if any, the two-dimensional real Landau-Ginzburg equation
possesses the Painleve property. For an ordinary differential equation to have
the Painleve property all of its solutions must be meromorphic but for partial
differential equations there are two inequivalent definitions, one a direct
investigation of a Laurent series expansion and the other indirect and relying
on a knowledge of the continuous symmetry group of the equation. We check both
methods for the Landau-Ginzburg equation in 2+1 dimensions and each one yields
that this equation does not possess the Painleve property for any values of the
parameters.
|
[
{
"version": "v1",
"created": "Sun, 14 Apr 1996 18:15:35 GMT"
}
] | 2008-02-03T00:00:00 |
[
[
"Stubbs",
"Daniel",
"",
"University of Western Ontario"
]
] |
solv-int/9604003
| null |
E. Alfinito, M. Leo, R. A. Leo, M. Palese and G. Soliani
|
Algebraic properties of the 1+1 dimensional Heisenberg spin field model
|
Tex file, 10 pages
|
Lett. Math. Phys., {\bf 32}, 241 (1994)
|
10.1007/BF00750666
| null |
solv-int nlin.SI
| null |
The Estabrook-Wahlquist prolongation method is applied to the (compact and
noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a
special realization (an algebra of the Kac-Moody type) of the arising
incomplete prolongation Lie algebra, a whole family of nonlinear field
equations containing the original Heisenberg system is generated.
|
[
{
"version": "v1",
"created": "Wed, 17 Apr 1996 17:04:57 GMT"
}
] | 2009-10-30T00:00:00 |
[
[
"Alfinito",
"E.",
""
],
[
"Leo",
"M.",
""
],
[
"Leo",
"R. A.",
""
],
[
"Palese",
"M.",
""
],
[
"Soliani",
"G.",
""
]
] |
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