Publication:
The Painleve approach for finding solitary wave solutions of nonlinear nonintegrable differential equations

Дата
2019
Авторы
Kudryashov, Nikolay A.
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Научные группы
Организационные подразделения
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Организационная единица
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
The approach by Painleve to construct the general solutions of some nonlinear second-order ordinary differential equations is generalized for finding exact solutions of nonintegrable differential equations. We demonstrate that this approach generalizes some other well-known algorithms of finding exact solutions: the tanh-function method, the G'/G-expansion method, the Exp-function method and some variants of the simplest equation method. The method allows us to search for both solution in the form of solitary waves and periodic solution expressed through elliptic functions. We demonstrate possibilities of the method for finding exact solutions of nonintegrable ordinary differential equations which are obtained as reductions of the modified Korteweg-de Vries equation with source, the generalized Burgers equation, the generalized Fisher equation, the generalized Gardner equation and the generalized Kuramoto-Sivashinsky equation.
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Цитирование
Kudryashov, Nikolay A. The Painleve approach for finding solitary wave solutions of nonlinear nonintegrable differential equations / Kudryashov, NikolayA // Optik. - 2019. - 183. - P. 642-649;. - 10.1016/j.ijleo.2019.02.087
URI
https://www.doi.org/10.1016/j.ijleo.2019.02.087
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85062330102&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000471739300085
 https://openrepository.mephi.ru/handle/123456789/18272
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