Simple Solutions of the Wave Equation with a Singularity at a Running Point, Based on the Complexified Bateman Solution

Аннотация

Simple explicit solutions of the homogeneous wave equation with constant propagation speed, having a power-like singularity at a moving space point, are constructed. The constructions are based on a complexified Bateman-type solution. An example of such a solution showing exponential decay with distance from the singular point is presented.