Publication:
Rational and Special Solutions for Some Painleve Hierarchies

Дата
2019
Авторы
Kudryashov, Nikolay 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
A self-similar reduction of the Korteweg-de Vries hierarchy is considered. A linear system of equations associated with this hierarchy is presented. This Lax pair can be used to solve the Cauchy problem for the studied hierarchy. It is shown that special solutions of the self-similar reduction of the KdV hierarchy are determined via the transcendents of the first Painleve hierarchy. Rational solutions are expressed by means of the Yablonskii-Vorob'ev polynomials. The map of the solutions for the second Painleve hierarchy into the solutions for the self-similar reduction of the KdV hierarchy is illustrated using the Miura transformation. Lax pairs for equations of the hierarchy for the Yablonskii-Vorob'ev polynomial are discussed. Special solutions to the hierarchy for the Yablonskii-Vorob'ev polynomials are given. Some other hierarchies with properties of the Painleve hierarchies are presented. The list of nonlinear differential equations whose general solutions are expressed in terms of nonclassical functions is extended.
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Kudryashov, Nikolay A. Rational and Special Solutions for Some Painleve Hierarchies / Kudryashov, NikolayA // Regular and Chaotic Dynamics. - 2019. - 24. - № 1. - P. 90-100;. - 10.1134/S1560354719010052
URI
https://www.doi.org/10.1134/S1560354719010052
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85061209063&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000457880700005
 https://openrepository.mephi.ru/handle/123456789/16541
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