English

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.

Keywords

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}
}
R2 v1 2026-06-22T01:42:54.567Z