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Recursion operators, conservation laws and integrability conditions for difference equations

Mikhailov, Alexander V., Wang, Jing Ping, Xenitidis, Pavlos (2011) Recursion operators, conservation laws and integrability conditions for difference equations. Theoretical and Mathematical Physics, 167 (1). pp. 421-443. ISSN 0040-5779. (doi:10.1007/s11232-011-0033-y) (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) (KAR id:28313)

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/s11232-011-0033-y

Abstract

We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler-Bobenko-Suris equations.

Item Type: Article
DOI/Identification number: 10.1007/s11232-011-0033-y
Uncontrolled keywords: difference equation, integrability, integrability condition, symmetry, conservation law, recursion operator
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: 24 Oct 2011 21:50 UTC
Last Modified: 06 Feb 2020 04:06 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/28313 (The current URI for this page, for reference purposes)
Wang, Jing Ping: https://orcid.org/0000-0002-6874-5629
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