Generalized and functional separable solutions to nonlinear delay Klein-Gordon equations

Polyanin, Andrei D. and Zhurov, Alexei I. 2014. Generalized and functional separable solutions to nonlinear delay Klein-Gordon equations. Communications in Nonlinear Science and Numerical Simulation 19 (8) , pp. 2676-2689. 10.1016/j.cnsns.2013.12.021

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Abstract

We describe a number of generalized separable, functional separable, and some other exact solutions to nonlinear delay Klein–Gordon equations of the form utt=kuxx+F(u,w),utt=kuxx+F(u,w), where u=u(x,t)u=u(x,t) and w=u(x,t-τ)w=u(x,t-τ), with ττ denoting the delay time. The generalized separable solutions are sought in the form View the MathML sourceu=∑n=1NΦn(x)Ψn(t), where the functions Φn(x)Φn(x) and Ψn(t)Ψn(t) are to be determined subsequently. Most of the equations considered contain one or two arbitrary functions of a single argument or one arbitrary function of two arguments of special form. We present a substantial number of new exact solutions, including periodic and antiperiodic ones, as well as composite solutions resulting from a nonlinear superposition of generalized separable and traveling wave solutions. All solutions involve free parameters (in some cases, infinitely many) and so can be suitable for solving certain problems and testing approximate analytical and numerical methods for nonlinear delay PDEs.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Medicine
Subjects:	R Medicine > R Medicine (General)
Publisher:	Elsevier
ISSN:	1007-5704
Date of Acceptance:	22 December 2013
Last Modified:	27 Mar 2019 14:35
URI:	https://orca.cardiff.ac.uk/id/eprint/79185

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