On integrability of a discrete analogue of Kaup - Kupershmidt equation

We study a new example of the equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of an one-dimensional lattice.We establish that in the continuous limit this new equation turns into the well-known Kaup-Kupershmidt equation.We also prove its integrability by constructing an 𝐿 -𝐴 pair and conservation laws.Moreover, we present a possibly new scheme for constructing conservation laws from 𝐿 -𝐴 pairs.We show that this new differential-difference equation is similar by its properties to the discrete Sawada-Kotera equation studied earlier.Their continuous limits, namely the Kaup-Kupershmidt and Sawada-Kotera equations, play the main role in the classification of fifth order evolutionary equations made by V.G.Drinfel'd, S.I.Svinolupov and V.V. Sokolov.