Classification of five-point differential-difference equations

2016/10/24 by R. N. Garifullin, R. I. Yamilov, D. Levi · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8121/aa5cc3

29 pages

arxiv created 2016/10/24 · arxiv updated 2017/04/05

Abstract

Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the discrete Sawada-Kotera equations. The resulting list contains 17 equations some of which seem to be new. We have found non-point transformations relating most of the resulting equations among themselves and their generalized symmetries.

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• On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations
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