Publication:
Lax Pairs and Rational Solutions of Similarity Reductions for Kupershmidt and Sawada – Kotera Hierarchies

Дата
2021
Авторы
Kudryashov, N. A.
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Научные группы
Организационные подразделения
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Аннотация
© 2021, Pleiades Publishing, Ltd.Self-similar reductions for equations of the Kupershmidt and Sawada – Kotera hierarchies areconsidered. Algorithms for constructing a Lax pairfor equations of these hierarchies are presented. Lax pairs for ordinary differentialequations of the fifth, seventh and eleventh orderscorresponding to the Kupershmidt and the Sawada – Kotera hierarchies are given.The Lax pairs allow us to solve these equations by means of the inversemonodromy transform method. The application of the Painlevé test to the seventh order of the similarity reduction for the Kupershmidt hierarchy isdemonstrated. It is shown that special solutions of the similarity reductions for the Kupershnmidt and Sawada – Kotera hierarchies are determined viathe transcendents of the K1 and K2 hierarchies. Rational solutions of the similarity reductions of the modified Kupershmidt and Sawada – Koterahierarchies are given. Special polynomials associated with the self-similar reductions ofthe Kupershmidt and Sawada – Kotera hierarchies are presented.Rational solutions of some hierarchies are calculated by means of the Miura transformations and taking into account special polynomials.
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Цитирование
Kudryashov, N. A. Lax Pairs and Rational Solutions of Similarity Reductions for Kupershmidt and Sawada – Kotera Hierarchies / Kudryashov, N.A. // Regular and Chaotic Dynamics. - 2021. - 26. - № 3. - P. 271-292. - 10.1134/S1560354721030059
URI
https://www.doi.org/10.1134/S1560354721030059
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85107117842&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000657859300005
 https://openrepository.mephi.ru/handle/123456789/25555
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