Abstract
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws are discussed. In a generic case, some of these conditions yield nonlocal conservation laws. A new integrable equation satisfying the second order integrability conditions is presented and its integrability is established by the construction of symmetries, conservation laws and a 3 × 3 Lax representation. Finally, via the relation of the symmetries of this equation to the Bogoyavlensky lattice, an integrable asymmetric quad equation and a consistent pair of difference equations are derived.
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Mikhailov, A.V., Xenitidis, P. Second Order Integrability Conditions for Difference Equations: An Integrable Equation. Lett Math Phys 104, 431–450 (2014). https://doi.org/10.1007/s11005-013-0668-8
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DOI: https://doi.org/10.1007/s11005-013-0668-8