Recursion operators,conservation laws,and integrability conditions for difference equations |
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Authors: | A V Mikhailov Jing Ping Wang P Xenitidis |
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Institution: | (1) Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401 1887, USA |
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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. |
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Keywords: | |
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