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.
"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