Darboux integrable discrete equations possessing an autonomous first-order integral
Exactly Solvable and Integrable Systems
2017-12-04 v1
Abstract
All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is obtained from a subclass of these equation via a non-point transformation. The general proposition on the symmetry structure of the quad-graph equations is proved as an auxiliary result.
Cite
@article{arxiv.1310.2282,
title = {Darboux integrable discrete equations possessing an autonomous first-order integral},
author = {S. Ya. Startsev},
journal= {arXiv preprint arXiv:1310.2282},
year = {2017}
}