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Exactly Solvable and Integrable Systems papers — page 29

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Discrete time Bogoyavlensky lattices
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…
Yu. B. SurisDec 20, 1995
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Integrable Models of the CFT on Hyper-Elliptic Surfaces
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…
S. A. Apikyan, C. J. EfthimiouDec 12, 1995
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On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation
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…
R. M. KashaevDec 11, 1995
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Estabrook-Wahlquist Prolongations and Infinite-Dimensional Algebras
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…
J. D. Finley, IIIDec 8, 1995
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On evolution of multiphase nonlinear modulated waves
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…
G. A. ElDec 6, 1995
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Binary nonlinearization for the Dirac systems
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…
Wen-Xiu MaDec 6, 1995
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A discrete time peakons lattice
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…
Yuri B. SurisDec 1, 1995
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Remarks on the Whitham equations
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…
Robert CarrollNov 24, 1995
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Properties of equations of the continuous Toda type
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 .…
E. Alfinito, G. Profilo, G. SolianiNov 23, 1995
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Algebra of Non-Local Charges in Supersymmetric Non-Linear Sigma Models
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…
L. E. Saltini, A. ZadraNov 16, 1995
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Classification of evolutionary equations on the lattice. I. The general theory
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form un,t = fn(un-1, un, un+1), where n is a discrete integer…
D. Levi, R. YamilovNov 16, 1995
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Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation
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…
Wen-Xiu Ma, Benno FuchssteinerNov 14, 1995
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Approximate Lie Group Analysis of Finite-difference Equations
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…
Azat M. LatypovNov 9, 1995
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A Novel Integration Scheme for Partial Differential Equations: an Application to the Complex Ginzburg-Landau Equation
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…
Alessandro Torcini, Helge Frauenkron, Peter GrassbergerNov 9, 1995
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Constructive building of the Lax pair in the non-linear sigma model
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…
Ariel O. Garcia, Roberto C. TrincheroNov 7, 1995
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Discrete soliton equations and convergence acceleration algorithms
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 η-algorithm is…
Atsushi Nagai, Junkichi SatsumaNov 7, 1995
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A three-by-three matrix spectral problem for AKNS hierarchy and its binary Nonlinearization
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…
Wen-Xiu Ma, Benno Fuchssteiner, Walter OevelNov 2, 1995
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Discrete Painleve equations: coalescences, limits and degeneracies
Starting from the standard form of the five discrete Painlevé equations we show how one can obtain (through appropriate limits) a host of new equations which are also the discrete analogues of the…
A. Ramani, B. GrammaticosNov 2, 1995
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The Gambier Mapping
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…
B. Grammaticos, A. RamaniOct 30, 1995
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On Integrable Models and their Interrelations
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…
H. Aratyn, E. Nissimov, S. PachevaOct 23, 1995
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The Orbit Method in the Finite Zone Integration Theory
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…
Petro Holod, Sergey KondratiukOct 23, 1995
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A discrete time relativistic Toda lattice
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…
Yuri B. SurisOct 23, 1995
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Toda Lattice Hierarchy and Zamolodchikov's Conjecture
In this letter, we show that certain Fredholm determinant D(λ;t), introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit of soliton solution for the Toda lattice hierarchy…
Saburo KakeiOct 23, 1995
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Conserved quantities for integrable chiral equations in 2+1 dimensions
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…
T. Ioannidou, R. S. WardOct 17, 1995
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Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system
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…
R. S. WardOct 17, 1995
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