 Commutation vector field for the wave equation

A first-order vector field $Z$ is a commutation field for the flat wave equation when $[\square ,Z]$ is zero or a controlled multiple of $\square$. Translations, spatial rotations and Lorentz boost vector fields commute with $\square$; the scaling vector field satisfies $[\square ,S]=2\square$. Repeated commutation preserves the differential order of a semilinear wave equation.