SIGMA, 2019, Volume 15, 062, 15 pp.
Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation
Rustem N. Garifullin, Ravil I. Yamilov
Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russia
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.
Miura transformation, integrable differential-difference equation, Ito–Narita–Bogoyavlensky equation.
|Russian Science Foundation
|RIY gratefully acknowledges the financial support from Russian Science Foundation grant (project 15-11-20007).
PDF file (399 kB)
MSC: 37K05, 37K10, 35G20
Received: April 1, 2019; in final form August 14, 2019; Published online August 23, 2019
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
Citation in format AMSBIB
\by Rustem~N.~Garifullin, Ravil~I.~Yamilov
\paper Integrable Modifications of the Ito--Narita--Bogoyavlensky Equation
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