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

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

2009-03-18

arxiv.org/abs/0903.3152v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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{\"a}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.

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