Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
Abstract
We consider five-point differential-difference equations. Our aim is to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications associated to transformations of the first, second and third orders. As far as we know, such a classification problem is solved for the first time in the discrete case. We analyze transformations obtained to specify their nature. A number of new integrable five-point equations and new transformations have been found. Moreover, we have derived one new completely discrete equation. There are a few non-standard transformations which are of the Miura type or are linearizable in a non-standard way. We have also proved that the orders of possible transformations are restricted by the number five in this problem.
Keywords
Cite
@article{arxiv.1903.11893,
title = {Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation},
author = {Rustem N. Garifullin and Ravil I. Yamilov},
journal= {arXiv preprint arXiv:1903.11893},
year = {2019}
}