English

Second order integrability conditions for difference equations. An integrable equation

Exactly Solvable and Integrable Systems 2015-06-16 v1

Abstract

Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation laws are also generated. A new integrable equation satisfying the second order integrability conditions is presented and its integrability is established by the construction of symmetries, conservation laws and a 3x3 Lax representation. Finally, the relation of the symmetries of this equation to a generalized Bogoyavlensky lattice and a new integrable lattice are derived.

Keywords

Cite

@article{arxiv.1305.4347,
  title  = {Second order integrability conditions for difference equations. An integrable equation},
  author = {Alexandre V. Mikhailov and Pavlos Xenitidis},
  journal= {arXiv preprint arXiv:1305.4347},
  year   = {2015}
}
R2 v1 2026-06-22T00:18:45.414Z