Symmetrically reduced Galileon equations and solutions

The maximally complicated arbitrary-dimensional “maximal” Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the $D$- to the two-dimensional (Monge-Ampere) equation, axial symmetry to its cubic extension, etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-$D$ solutions.