Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation

Rustem N. Garifullin ; Ravil I. Yamilov

Symmetry, integrability and geometry: methods and applications, Tome 15 (2019)

Résumé

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.

Détail

Keywords: integrable differential-difference equation, Ito–Narita–Bogoyavlensky equation.
Mots-clés : Miura transformation

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