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arXiv · 1903.11893

Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation

Rustem N. Garifullin·Ravil I. Yamilov
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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.

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Rustem N. Garifullin, Ravil I. Yamilov. 2019-08-23. Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation. https://doi.org/10.3842/sigma.2019.062

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