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.
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}
}