Non-trivial Soliton Scattering in Planar Integrable Systems

TL;DR

This paper reviews two-dimensional integrable systems derived from self-dual Yang-Mills-Higgs equations, highlighting their non-trivial soliton scattering behaviors contrary to typical expectations of trivial scattering in integrable theories.

Contribution

It provides an extended review of non-trivial soliton scattering phenomena in planar integrable systems derived from higher-dimensional theories.

Findings

Soliton scattering in these systems is highly non-trivial.

Derived from self-dual Yang-Mills-Higgs equations.

Contrasts with the usual trivial scattering in integrable models.

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.