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

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 - 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 ) 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.