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arXiv · 1305.0588

Darboux transformations and Recursion operators for differential--difference equations

Farbod Khanizadeh·Alexander V. Mikhailov·Jing Ping Wang
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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.

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Farbod Khanizadeh, Alexander V. Mikhailov, Jing Ping Wang. 2013-05-02. Darboux transformations and Recursion operators for differential--difference equations. https://doi.org/10.1007/s11232-013-0124-z

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