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

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

2009-02-23

arxiv.org/abs/0902.3954v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, for the proceedings of the 4th Workshop "Group Analysis of Differential Equations and Integrable Systems", Cyprus, 2

Scientific paper

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{\"a}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.

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