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This article is cited in 1 scientific paper (total in 1 paper)
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
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:
Miura transformation, integrable differential-difference equation, Ito–Narita–Bogoyavlensky equation.
Received: April 1, 2019; in final form August 14, 2019; Published online August 23, 2019
Citation:
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1498 https://www.mathnet.ru/eng/sigma/v15/p62
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