Free wave equation

The free wave equation on $R^{1+d}$ is given by

$\Box f=0$

where f is a scalar or vector field on Minkowski space $R^{1+d}$. In coordinates, this becomes

$-\partial _{tt}f+\Delta f=0.$

It is the prototype for many nonlinear wave equations.

One can add a mass term to create the Klein-Gordon equation.