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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 3, Pages 158–164 (Mi ufa383)  

This article is cited in 1 scientific paper (total in 1 paper)

On integrability of a discrete analogue of Kaup–Kupershmidt equation

R. N. Garifullin, R. I. Yamilov

Institute of Mathematics, Ufa Scientific Center, RAS, Chenryshevsky str. 112, 450008, Ufa, Russia

Abstract: 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.

Keywords: differential-difference equation, integrability, Lax pair, conservation law.

Funding Agency Grant Number
Russian Science Foundation 15-11-20007
The research is supported by the Russian Science Foundation (project no. 15-11-20007).


Full text: PDF file (360 kB)
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English version:
Ufa Mathematical Journal, 2017, 9:3, 158–164 (PDF, 361 kB); https://doi.org/10.13108/2017-9-3-158

Bibliographic databases:

UDC: 517.9
MSC: 37K10, 35G50, 39A10
Received: 12.12.2016
Language:

Citation: R. N. Garifullin, R. I. Yamilov, “On integrability of a discrete analogue of Kaup–Kupershmidt equation”, Ufimsk. Mat. Zh., 9:3 (2017), 158–164; Ufa Math. J., 9:3 (2017), 158–164

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations II”, J. Phys. A-Math. Theor., 51:6 (2018), 065204  crossref  mathscinet  zmath  isi  scopus
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