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

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dc.contributor.authorZhurov, A. I.
dc.contributor.authorPolyanin, A. D.
dc.date.accessioned2024-11-25T16:20:56Z
dc.date.available2024-11-25T16:20:56Z
dc.date.issued2020
dc.description.abstractThe 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.
dc.format.extentС. 227-242
dc.identifier.citationZhurov, 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
dc.identifier.doi10.1080/14029251.2020.1700633
dc.identifier.urihttps://www.doi.org/10.1080/14029251.2020.1700633
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85079233689&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000509684400004
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/20294
dc.relation.ispartofJournal of Nonlinear Mathematical Physics
dc.titleSymmetry reductions and new functional separable solutions of nonlinear Klein-Gordon and telegraph type equations
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue2
oaire.citation.volume27
relation.isOrgUnitOfPublicationdcdb137c-0528-46a5-841b-780227a67cce
relation.isOrgUnitOfPublication.latestForDiscoverydcdb137c-0528-46a5-841b-780227a67cce
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