Abstract
We consider nonlinear wave type PDEs with delay of the form utt+H1(u)ut=[G(u)ux]x+H2(u)ux+F(u,w),where u=u(x,t) is the unknown function, w=u(x,t−τ), and τ is the delay time. The source function F(u,w) depends on one or several arbitrary functions of one argument. Using the modified method of functional constraints, we obtain a number of new exact solutions with generalized and functional separation of variables, as well as traveling-wave solutions. Most solutions are expressed in terms of elementary functions and contain free parameters. These solutions can be used to formulate test problems intended to evaluate the accuracy of numerical methods for solving nonlinear delay PDEs.
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