Kirchhoff formula

In three spatial dimensions, the solution with initial position $u_0$ and velocity $u_1$ iswhere $M_t$ is the spherical mean.

The strong Huygens principle says that the three-dimensional wave solution at $(t,x)$ depends only on initial data on the sphere $|y-x|=|t|$. A compactly supported disturbance therefore leaves no tail in the interior of its light cone.