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Recursion operators, conservation laws, and integrability conditions for difference equations

Mikhailov, AV, Wang, JP and Xenitidis, P (2011) Recursion operators, conservation laws, and integrability conditions for difference equations. Theoretical and Mathematical Physics, 167 (1). 421 - 443 . ISSN 1573-9333

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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
Keywords: difference equations, integrability, integrability conditions, symmetries, conservation law, recursion operator
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 25 Oct 2011 08:52
Last Modified: 08 Feb 2013 17:34
Published Version: http://dx.doi.org/10.1007/s11232-011-0033-y
Status: Published
Publisher: Springer
Identification Number: 10.1007/s11232-011-0033-y
URI: http://eprints.whiterose.ac.uk/id/eprint/43354

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