Abstract
We study a new example of a lattice equation, which is one of the key equations of a generalized symmetry classification of five-point differential-difference equations. This equation has two different continuum limits, which are the well-known fifth-order partial-differential equations, namely, the Sawada–Kotera and Kaup-Kupershmidt equations. We justify its integrability by constructing an L-A pair and a hierarchy of conservation laws.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 152, Mathematical Physics, 2018.
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Garifullin, R.N., Yamilov, R.I. On the Integrability of Lattice Equations with Two Continuum Limits. J Math Sci 252, 283–289 (2021). https://doi.org/10.1007/s10958-020-05160-x
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DOI: https://doi.org/10.1007/s10958-020-05160-x