Discrete potential Ablowitz–Kaup–Newell–Segur equation

DOI10.1080/10236198.2019.1662410zbMath1423.39014OpenAlexW2973219597MaRDI QIDQ5240629

Song-Lin Zhao

Publication date: 29 October 2019

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2019.1662410

zbMATH Keywords

solutionscontinuum limitreductiongeneralized Cauchy matrix approachdiscrete AKNS equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Discrete version of topics in analysis (39A12) Partial difference equations (39A14)

Cites Work

• Linear integral equations and nonlinear difference-difference equations
• On Hirota's difference equations
• On some linear integral equations generating solutions of nonlinear partial differential equations
• Classification of integrable equations on quad-graphs. The consistency approach
• The Sylvester equation and integrable equations: the Ablowitz-Kaup-Newell-Segur system
• The discrete and continuous Painlevé VI hierarchy and the Garnier systems
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Discrete Systems and Integrability
• Integrable symplectic maps associated with the ZS-AKNS spectral problem
• Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach
• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• Symmetries for the Ablowitz-Ladik Hierarchy: Part II. Integrable Discrete Nonlinear Schrödinger Equations and Discrete AKNS Hierarchy
• A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• A Nonlinear Difference Scheme and Inverse Scattering
• On the Solution of a Class of Nonlinear Partial Difference Equations
• Bäcklund transformation for the Krichever-Novikov equation
• Direct Linearization of Extended Lattice BSQ Systems
• The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation
• A discrete negative AKNS equation: generalized Cauchy matrix approach
• Symmetry Constraint of the Differential-difference KP Hierarchy and a Second Discretization of the ZS-AKNS System

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