  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.
