Publication:
Symmetry reductions and new functional separable solutions of nonlinear Klein-Gordon and telegraph type equations

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W3003390691.pdf(434.4 KB)
Дата
2020
Авторы
Zhurov, A. I.
Polyanin, A. D.
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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
The paper is concerned with different classes of nonlinear Klein-Gordon and telegraph type equations with variable coefficients c(x)u(tt) + d(x)u(t) = [a(x)u(x)](x) + b(x)u(x) + p(x) f (u), where f (u) is an arbitrary function. We seek exact solutions to these equations by the direct method of symmetry reductions using the composition of functions u = U (z) with z = phi (x, t). We show that f (u) and any four of the five functional coefficients a(x), b(x), c(x), d(x), and p(x) in such equations can be set arbitrarily, while the remaining coefficient can be expressed in terms of the others. The study investigates the properties and finds some solutions of the overdetermined system of PDEs for phi (x, t). Examples of specific equations with new exact functional separable solutions are given. In addition, the study presents some generalized traveling wave solutions to more complex, nonlinear Klein-Gordon and telegraph type equations with delay.
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Цитирование
Zhurov, A. I. Symmetry reductions and new functional separable solutions of nonlinear Klein-Gordon and telegraph type equations / Zhurov, AI, Polyanin, AD // Journal of Nonlinear Mathematical Physics. - 2020. - 27. - № 2. - P. 227-242. - 10.1080/14029251.2020.1700633
URI
https://www.doi.org/10.1080/14029251.2020.1700633
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85079233689&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000509684400004
 https://openrepository.mephi.ru/handle/123456789/20294
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