Darboux transformations and Recursion operators for differential--difference equations
Exactly Solvable and Integrable Systems
2015-06-15 v1
Abstract
In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensive list of integrable differential-difference equations together with their Hamiltonian structures, recursion operators, nontrivial generalised symmetries and Darboux-Lax representations. The new results include multi-Hamiltonian structures and recursion operators for integrable Volterra type equations, integrable discretization of derivative nonlinear Schr\"odinger equations such as the Kaup-Newell lattice, the Chen-Lee-Liu lattice and the Ablowitz-Ramani-Segur (Gerdjikov-Ivanov) lattice. We also compute the weakly nonlocal inverse recursion operators.
Cite
@article{arxiv.1305.0588,
title = {Darboux transformations and Recursion operators for differential--difference equations},
author = {Farbod Khanizadeh and Alexander V. Mikhailov and Jing Ping Wang},
journal= {arXiv preprint arXiv:1305.0588},
year = {2015}
}