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Construction of functional separable solutions in implicit form for non-linear Klein–Gordon type equations with variable coefficients

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1-s2.0-S0020746219301210-main.pdf(615.42 KB)
Дата
2019
Авторы
Polyanin, A. D.
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Организационные подразделения
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Институт интеллектуальных кибернетических систем
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© 2019 Elsevier Ltd The paper deals with non-linear Klein–Gordon type equations c(x)u tt =[a(x)f(u)u x ] x +b(x)g(u).The direct method for constructing functional separable solutions in implicit form to non-linear PDEs is used. This effective method is based on the representation of solutions in the form ∫h(u)du=ξ(x)ω(t)+η(x),where the functions h(u), ξ(x), η(x), and ω(t)are determined further by analyzing the resulting functional-differential equations. Examples of specific Klein–Gordon type equations and their exact solutions are given. The main attention is paid to non-linear equations of a fairly general form, which contain several arbitrary functions dependent on the unknown u and /or the spatial variable x (it is important to note that exact solutions of non-linear PDEs, that contain arbitrary functions and therefore have significant generality, are of great practical interest for testing various numerical and approximate analytical methods for solving corresponding initial–boundary value problems). Many new generalized traveling-wave solutions and functional separable solutions (in closed form)are described. Solutions of several Klein–Gordon equations with delay are also given.
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Polyanin, A. D. Construction of functional separable solutions in implicit form for non-linear Klein–Gordon type equations with variable coefficients / Polyanin, A. D. // International Journal of Non-Linear Mechanics. - 2019. - 114. - P. 29-40. - 10.1016/j.ijnonlinmec.2019.04.005
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https://www.doi.org/10.1016/j.ijnonlinmec.2019.04.005
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85064829120&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000469904900005
 https://openrepository.mephi.ru/handle/123456789/16323
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