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Darboux transformations and recursion operators for differential-difference equations

Khanizadeh, F., Mikhailov, Alexander V., Wang, Jing Ping (2013) Darboux transformations and recursion operators for differential-difference equations. Theoretical and Mathematical Physics, 177 (3). pp. 1606-1654. ISSN 0040-5779. (doi:10.1007/s11232-013-0124-z) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1007/s11232-013-0124-z

Abstract

We review two concepts directly related to the Lax representations of integrable systems: Darboux transformations and recursion operators. We present an extensive list of integrable differential-difference equations with their Hamiltonian structures, recursion operators, nontrivial generalized symmetries, and Darboux-Lax representations. The new results include multi-Hamiltonian structures and recursion operators for integrable Volterra-type equations and integrable discretizations of derivative nonlinear Schrödinger equations such as the Kaup-Newell, Chen-Lee-Liu, and Ablowitz-Ramani-Segur (Gerdjikov-Ivanov) lattices. We also compute the weakly nonlocal inverse recursion operators.

Item Type: Article
DOI/Identification number: 10.1007/s11232-013-0124-z
Uncontrolled keywords: symmetry, recursion operator, bi-Hamiltonian structure, Darboux transformation, Lax representation, integrable equation
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Jing Ping Wang
Date Deposited: 14 Jan 2014 13:45 UTC
Last Modified: 06 Feb 2020 04:08 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/37800 (The current URI for this page, for reference purposes)
Wang, Jing Ping: https://orcid.org/0000-0002-6874-5629
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