Publication:
Nonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source

Дата
2019
Авторы
Kudryashov, N. A.
Safonova, D. V.
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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
© 2019 John Wiley & Sons, Ltd.The method for constructing first integrals and general solutions of nonlinear ordinary differential equations is presented. The method is based on index accounting of the Fuchs indices, which appeared during the Painlevé test of a nonlinear differential equation. The Fuchs indices indicate us the leading members of the first integrals for the origin differential equation. Taking into account the values of the Fuchs indices, we can construct the auxiliary equation, which allows to look for the first integrals of nonlinear differential equations. The method is used to obtain the first integrals and general solutions of the KdV-Burgers and the mKdV-Burgers equations with a source. The nonautonomous first integrals in the polynomials form are found. The general solutions of these nonlinear differential equations under at some additional conditions on the parameters of differential equations are also obtained. Illustrations of some solutions of the KdV-Burgers and the mKdV-Burgers are given.
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Kudryashov, N. A. Nonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source / Kudryashov, N.A., Safonova, D.V. // Mathematical Methods in the Applied Sciences. - 2019. - 10.1002/mma.5684
URI
https://www.doi.org/10.1002/mma.5684
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85066913962&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000475396600015
 https://openrepository.mephi.ru/handle/123456789/18217
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