Darboux transformations and Recursion operators for differential--difference equations

2013/05/02 by Farbod Khanizadeh, Alexander V. Mikhailov, Jing Ping Wang · 3 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1007/s11232-013-0124-z

arxiv created 2013/05/02 · arxiv updated 2015/06/15

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 Schrödinger 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.

Cited by

• Arithmetic Supports of Lax Difference Hierarchies
• On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations
• The gauge action on semi-discrete Lax representations and its invariants

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