Geodesic
On the Integrability of a Lattice Equation with Two Continuum Limits
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 159-164

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We study a new example of lattice equation being one of the key equations of a recent 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.
Keywords: differential-difference equation, integrability, conservation law.
Mots-clés : Lax pair 
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     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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R. N. Garifullin; R. I. Yamilov. On the Integrability of a Lattice Equation with Two Continuum Limits. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 159-164. http://geodesic.mathdoc.fr/item/INTO_2018_152_a13/