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\"acklund 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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