On consistent systems of difference equations
Exactly Solvable and Integrable Systems
2020-01-08 v1 Dynamical Systems
Abstract
We consider overdetermined systems of difference equations for a single function which are consistent, and propose a general framework for their analysis. The integrability of such systems is defined as the existence of higher order symmetries in both lattice directions and various examples are presented. Two hierarchies of consistent systems are constructed, the first one using lattice paths and the second one as a deformation of the former. These hierarchies are integrable and their symmetries are related via Miura transformations to the Bogoyavlensky and the discrete Sawada-Kotera lattices, respectively.
Cite
@article{arxiv.1906.03898,
title = {On consistent systems of difference equations},
author = {Pavlos Xenitidis},
journal= {arXiv preprint arXiv:1906.03898},
year = {2020}
}
Comments
10 pages, 2 figures