Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays

The study gives a brief overview of publications on exact solutions for functional PDEs with delays various types and methods constructing such solutions. For the first time, second-order wave-type nonlinear source term containing unknown function proportional time delay, space or both are considered. In addition to constant speed, equations variable speed also studied. New one-dimensional reductions delay obtained using simpler without separation variables PDEs. Self-similar solutions, additive multiplicative separable generalized some other presented. More complex general form investigated. Overall, more than thirty that admit described. results can be used test numerical investigate properties considered related delays.