  The behavior of solitons in integrable theories is strongly constrained by
the integrability of the theory, that is by the existence of an infinite number
of conserved quantities that these theories are known to possess. As a result
the soliton scattering of such theories are expected to be trivial (with no
change of direction, velocity or shape). In this paper we present an extended
review on soliton scattering of two spatial dimensional integrable systems
which have been derived as dimensional reductions of the self-dual
Yang-Mills-Higgs equations and whose scattering properties are highly
non-trivial.
