Non-trivial Soliton Scattering in Planar Integrable Systems

Abstract

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.