We consider the Cauchy problem for the wave equation in the whole space ℝn, with initial data that are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of the solutions to the wave equation.
Mark L. Agranovsky. Eric Todd Quinto. "Geometry of stationary sets for the wave equation in ℝn: The case of finitely supported initial data." Duke Math. J. 107 (1) 57 - 84, 1 March 2001. https://doi.org/10.1215/S0012-7094-01-10714-X