On the integrability of a discrete analogue of the Kaup-Kupershmidt equation

2016/12/12 by Garifullin, R. N., Yamilov, R. I.
#35G50 #37K10 #39A10 #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1612.03652

Abstract

We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimensional lattice. We have established that in the continuous limit this new equation goes into the well-known Kaup-Kupershmidt equation. We have also proved its integrability by constructing an L-A pair and conservation laws. Moreover, we present a possibly new scheme for deriving conservation laws from L-A pairs.

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