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

摘要

We present a number of exact multiplicative and additive separable solutions to nonlinear delay reaction-diffusion equations of the form u_t =ku_(xx) + F(u,w), where u = u(x, t), w = u(x, t - t), and t 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) 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.