Caustics for Spherical Waves
  We study the development of caustics in shift-symmetric scalar field theories
by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of
space dimensions. We show that the pure Galileon, the DBI-Galileon, and the
extreme-relativistic Galileon naturally emerge as the unique set of
caustic-free theories, highlighting a link between the caustic-free condition
for simple $SO(p)$-waves and the existence of either a global Galilean symmetry
or a global (extreme-)relativistic Galilean symmetry.
