Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case

Abstract

We consider the partial difference equations of the Adler-Bobenko-Suris classification, which are characterized as multidimensionally consistent. The latter property leads naturally to the construction of auto-B{ä}cklund transformations and Lax pairs for all the equations in this class. Their symmetry analysis is presented and infinite hierarchies of generalized symmetries are explicitly constructed.

16 pages, for the proceedings of the 4th Workshop "Group Analysis of Differential Equations and Integrable Systems", Cyprus, 2008

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• On the Lagrangian formulation of multidimensionally consistent systems
• Darboux transformation with Dihedral reduction group
• Symmetries of the Continuous and Discrete Krichever-Novikov Equation
• A new recursion operator for the Viallet equation
• Darboux transformations with tetrahedral reduction group and related integrable systems
• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• Classification of integrable discrete Klein-Gordon models
• An algebraic method of classification of S-integrable discrete models
• A non autonomous generalization of the $Q_{\text{V}}$ equation
• Algebraic entropy for systems of quad equations
• Classification of integrable boundary equations for integrable quad-graph systems
• Invariant manifolds for the hyperbolic type integrable equations and their applications