Second Order Integrability Conditions for Difference Equations: An Integrable Equation |
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Authors: | Alexandre V Mikhailov Pavlos Xenitidis |
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Institution: | 1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK
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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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