Asymmetric integrable quad-graph equations

DOI10.1080/00036810903329951zbMath1188.37059arXiv0906.2339OpenAlexW2105557366WikidataQ58159103 ScholiaQ58159103MaRDI QIDQ3558504

Claude Viallet, Peter E. Hydon

Publication date: 5 May 2010

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2339

zbMATH Keywords

conservation lawsintegrable systemsdifference equationsalgebraic entropy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12)

Related Items (9)

A direct algorithm for constructing recursion operators and Lax pairs for integrable models ⋮ Gambier lattices and other linearisable systems ⋮ Algebraic entropy of (integrable) lattice equations and their reductions ⋮ Singularity confinement property for the (non-autonomous) Adler-Bobenko-Suris integrable lattice equations ⋮ Linear degree growth in lattice equations ⋮ Classification of 3D Consistent Quad-Equations ⋮ From Yang-Baxter Maps to Integrable Recurrences ⋮ On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations ⋮ Difference systems in bond and face variables and non-potential versions of discrete integrable systems

Cites Work

• Unnamed Item
• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• Lax pair for the Adler (lattice Krichever-Novikov) system
• Integrable lattice equations and their growth properties
• Singularity, complexity, and quasi-integrability of rational mappings
• Algebraic entropy
• Bilinearization of discrete soliton equations and singularity confinement.
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
• Deconstructing an integrable lattice equation
• Conservation laws for NQC-type difference equations
• INTEGRABLE LATTICE MAPS: Q_V, A RATIONAL VERSION OF Q₄
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• The lattice Gel'fand-Dikii hierarchy
• A new two-dimensional lattice model that is  consistent around a cube
• Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
• Do integrable mappings have the Painlevé property?
• Conservation laws for integrable difference equations

This page was built for publication: Asymmetric integrable quad-graph equations