Journal ArticleDOI
Method for Generating Discrete Soliton Equation. III
TLDR
As a continuation of previous work, discretization of nonlinear Schrodinger equation and its analogues are discussed as the reduction of 2-component KP hierarchy.Abstract:
As a continuation of previous work, discretization of nonlinear Schrodinger equation and its analogues are discussed as the reduction of 2-component KP hierarchyread more
Citations
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The discrete Korteweg-de Vries equation
Frank W. Nijhoff,H.W. Capel +1 more
TL;DR: In this paper, different aspects of integrable discretizations in space and time of the Korteweg-de Vries equation are reviewed, including Miura transformations, connections to integrably mappings, similarity reductions and discrete versions of Painleve equations as well as connections to Volterra systems.
Journal ArticleDOI
Quantum Integrable Models and Discrete Classical Hirota Equations
TL;DR: In this article, the functional relation for commuting quantum transfer matrices of quantum integrable models is shown to coincide with classical Hirota's bilinear difference equation, which is equivalent to the completely discretized classical 2D Toda lattice with open boundaries.
Journal ArticleDOI
T-systems and Y-systems in integrable systems*
TL;DR: In this paper, a collection of short reviews on Toda field equations on discrete spacetime, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe- ansatze, quantum transfer matrix method and so forth.
Journal ArticleDOI
Linear integral equations and nonlinear difference-difference equations
TL;DR: In this article, a method to obtain various integrable nonlinear difference-difference equations and the associated linear integral equations from which their solutions can be inferred is presented, which can be regarded as arising from Bianchi identities expressing the commutativity of Backlund transformations.
References
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Journal ArticleDOI
Exact envelope‐soliton solutions of a nonlinear wave equation
TL;DR: In this article, exact N-envelope-soliton solutions have been obtained for the following nonlinear wave equation, where α, β, γ and δ are real positive constants with the relation αβ = γδ.
Journal ArticleDOI
Basic representations of affine Lie algebras and dual resonance models
Igor Frenkel,Victor G. Kac +1 more
Journal ArticleDOI
Nonlinear differential−difference equations
Mark J. Ablowitz,J. F. Ladik +1 more
TL;DR: In this paper, a new discrete eigenvalue problem has been introduced to obtain and solve certain classes of nonlinear differential-difference equations, which can be obtained by inverse scattering.
Journal ArticleDOI
Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type
TL;DR: In this paper, a new approach to soliton equations, based on τ functions (or Hirota's dependent variables), vertex operators and the Clifford algebra of free fermions, is applied to study a new hierarchy of Kadomtsev-Petviashvili type equations (the BKP hierarchy).
Journal ArticleDOI
Discrete Analogue of a Generalized Toda Equation
TL;DR: In this paper, a discrete analogue of a generalized Toda equation and its Backlund transformations are obtained, where the equation is expressed with the bilinear form as follows, where Z i and D i for i = 1, 2, 3, are an arbitrary parameter and a linear combination of the binary operators D t, D x, D y, D n, etc.