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This article is cited in 8 scientific papers (total in 8 papers)
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.
Received: 12.12.2016
Citation:
R. N. Garifullin, R. I. Yamilov, “On integrability of a discrete analogue of Kaup–Kupershmidt equation”, Ufa Math. J., 9:3 (2017), 158–164
Linking options:
https://www.mathnet.ru/eng/ufa383https://doi.org/10.13108/2017-9-3-158 https://www.mathnet.ru/eng/ufa/v9/i3/p158
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