Soliton Solutions and Nontrivial Scattering in an Integrable Chiral Model in (2+1) Dimensions

TL;DR

This paper presents new soliton solutions in an integrable (2+1)-dimensional chiral model, revealing complex scattering behaviors such as nontrivial angles and elastic collisions, challenging the usual expectation of trivial scattering in integrable theories.

Contribution

The authors introduce novel soliton solutions with nontrivial scattering properties in an integrable chiral model, demonstrating complex interaction phenomena.

Findings

Soliton scattering angles of π/N in head-on collisions

Elastic scattering in soliton-antisoliton interactions

Head-on soliton-antisoliton collision results in 90° scattering

Abstract

The behaviour of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e. by the existence of an infinite number of conserved quantities which these theories are known to possess. One usually expects the scattering of solitons in such theories to be rather simple, i.e. trivial. By contrast, in this paper we generate new soliton solutions for the planar integrable chiral model whose scattering properties are highly nontrivial; more precisely, in head-on collisions of $N$ indistinguishable solitons the scattering angle (of the emerging structures relative to the incoming ones) is $\pi/N$. We also generate soliton-antisoliton solutions with elastic scattering; in particular, a head-on collision of a soliton and an antisoliton resulting in $90^0$ scattering.