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

2009/02/23 by Pavlos Xenitidis, P. Xenitidis, Xenitidis, P.
Chemistry · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.0902.3954

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

arxiv created 2009/02/23 · openalex publication_date 2009/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Bäcklund 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.

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