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 formut=kuxx+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.