We examine how the breaking of shift symmetry affects the formation of
caustics for the standard canonical kinetic theory as well as for the DBI
theory. We show in this case, that the standard canonical kinetic theory is
caustic free but the same does not always apply for the DBI model. We make
similar arguments about the Conformal Galileons. Finally, it is shown that the
simple wave condition is not invariant under field redefinitions and the
meaning of simple waves after symmetry breaking is discussed.