  We study the scattering processes of kink-antikink and kink-kink pairs in a
field theory model with non-differentiable potential at its minima. The
kink-antikink scattering includes cases of capture and escape of the soliton
pair separated by a critical velocity, without windows of multi bounce followed
by escape. Around the critical velocity, the behavior is fractal. The emission
of radiation strongly influences the small velocity cases, with the most
radiative cases being also the most chaotic. The radiation appears through the
emission of compact oscillons and the formation of compact shockwaves. The
kink-kink scattering happens elastically, with no emission of radiation. Some
features of both the kink-antikink and the kink-kink scattering are explained
using a collective coordinate model, even though the kink-kink case exhibits a
null-vector problem.
