English

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

Exactly Solvable and Integrable Systems 2015-05-13 v1

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{\"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.

Keywords

Cite

@article{arxiv.0903.3152,
  title  = {Symmetries and integrability of discrete equations defined on a black-white lattice},
  author = {P. D. Xenitidis and V. G. Papageorgiou},
  journal= {arXiv preprint arXiv:0903.3152},
  year   = {2015}
}

Comments

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