Geodesic
Recursion operators, conservation laws, and integrability conditions for difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 23-49
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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 equation, integrability, integrability condition, symmetry, conservation law, recursion operator. 
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A. V. Mikhailov; J. P. Wang; P. Xenitidis. Recursion operators, conservation laws, and integrability conditions for difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 23-49. http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a1/

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