Symmetries and integrability of discrete equations defined on a black-white lattice

Abstract

We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda type equations. Their multidimensional consistency leads to B{ä}cklund transformations relating different members of this class, as well as to Lax pairs. Their symmetry analysis is presented yielding infinite hierarchies of generalized symmetries.

12 pages, submitted to the special issue on "Symmetries and Integrability of Difference Equations" of J. Phys. A: Math. Theor

References in corpus (2)

• Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions
• Continuous symmetric reductions of the Adler-Bobenko-Suris equations

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