Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Rustem N. Garifullin¹  Ravil I. Yamilov¹ 

[1] Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences

关键词: Miura transformation;    integrable differential-difference equation;    Ito–Narita– Bogoyavlensky equation;   

DOI  :  10.3842/SIGMA.2019.062

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown