Exact separable solutions of delay reaction-diffusion equations and other nonlinear partial functional-differential equations

Polyanin, Andrei D. and Zhurov, Alexei I. 2014. Exact separable solutions of delay reaction-diffusion equations and other nonlinear partial functional-differential equations. Communications in Nonlinear Science and Numerical Simulation 19 (3) , pp. 409-416. 10.1016/j.cnsns.2013.07.019

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Abstract

We present a number of exact multiplicative and additive separable solutions to nonlinear delay reaction–diffusion equations of the form ut=kuxx+F(u,w),ut=kuxx+F(u,w), where u=u(x,t)u=u(x,t), w=u(x,t-τ)w=u(x,t-τ), and τ is the delay time. All of the equations involve one arbitrary function of one argument. We also give a number of exact solutions to more complex nonlinear partial functional-differential equations with a time-varying delay τ=τ(t)τ=τ(t) as well as to equations with several delay times. We extend the results to nonlinear partial differential–difference equations containing arbitrary linear differential operators of any order in the independent variables x and t; in particular, these equations include the nonlinear delay Klein–Gordon equation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Medicine
Subjects:	R Medicine > R Medicine (General)
Publisher:	Elsevier
ISSN:	1007-5704
Date of Acceptance:	16 July 2013
Last Modified:	27 Mar 2019 14:34
URI:	https://orca.cardiff.ac.uk/id/eprint/79184

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