On group and phase velocities manifested through exact solutions to the equations of some propagation phenomena

A system of non-Hermite, non-orthogonal functions that are new for concrete applications is introduced to generate explicit and previously unknown, physically meaningful solutions for bar and plate equations. The approach allows in some cases to establish completeness of these sets of solutions. Various other separate results technically related to these basic development are presented. In the available literature there are no registered efforts to extract the two velocities from exact solutions of the equations of the processes in which the two parameters are explicitly present.