Abstract
We present a new method for constructing exact solutions of nonlinear delay PDEs using special solutions of simpler auxiliary PDEs without delay. The application of the method is demonstrated on nonlinear reaction–diffusion and wave-type equations with delay that include variable coefficients and arbitrary functions. New generalized traveling-wave solutions and functional separable solutions in implicit form are obtained. Results of the paper can be used to formulate test problems intended to verify the adequacy and evaluate the accuracy of numerical and approximate analytical methods of solving the corresponding nonlinear initial-boundary value problems with delay.
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