Cosymmetries and Nijenhuis recursion operators for difference equations
Exactly Solvable and Integrable Systems
2015-05-19 v1
Abstract
In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion operator for the Viallet equation. Moreover, we show that this operator is Nijenhuis and thus generates infinitely many commuting local symmetries. This recursion operator and its factorisation into Hamiltonian and symplectic operators can be applied to Yamilov's discretisation of the Krichever-Novikov equation.
Cite
@article{arxiv.1009.2403,
title = {Cosymmetries and Nijenhuis recursion operators for difference equations},
author = {Alexander V. Mikhailov and Jing Ping Wang and Pavlos Xenitidis},
journal= {arXiv preprint arXiv:1009.2403},
year = {2015}
}