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arXiv · 1305.4347

Second order integrability conditions for difference equations. An integrable equation

Alexandre V. Mikhailov·Pavlos Xenitidis
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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 is discussed. In the generic case, nonlocal conservation laws are also generated. 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 3x3 Lax representation. Finally, the relation of the symmetries of this equation to a generalized Bogoyavlensky lattice and a new integrable lattice are derived.

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Alexandre V. Mikhailov, Pavlos Xenitidis. 2013-05-19. Second order integrability conditions for difference equations. An integrable equation. https://doi.org/10.1007/s11005-013-0668-8

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