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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
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
Аннотация:
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.
Ключевые слова:
Miura transformation, integrable differential-difference equation, Ito–Narita–Bogoyavlensky equation.
Поступила: 1 апреля 2019 г.; в окончательном варианте 14 августа 2019 г.; опубликована 23 августа 2019 г.
Образец цитирования:
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1498 https://www.mathnet.ru/rus/sigma/v15/p62
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