Recursion operators, conservation laws and integrability conditions for difference equations - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




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Abstract: In this paper we make an attempt to give a consistent background anddefinitions suitable for the theory of integrable difference equations. Weadapt a concept of recursion operator to difference equations and show that itgenerates an infinite sequence of symmetries and canonical conservation lawsfor a difference equation. Similar to the case of partial differentialequations these canonical densities can serve as integrability conditions fordifference equations. We have found the recursion operators for the Viallet andall ABS equations.



Author: Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis

Source: https://arxiv.org/



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