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
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.
|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:||13 Oct 2016 07:42|