Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions

TL;DR

This paper explores noncommutative sigma models in 2+1 dimensions, constructing multi-soliton and soliton-antisoliton solutions using dressing transformations, and analyzing their scattering behaviors.

Contribution

It introduces an iterative dressing method for generating multi-soliton and soliton-antisoliton solutions in a noncommutative sigma model, including explicit collision angle analyses.

Findings

Constructed multi-soliton and soliton-antisoliton solutions.

Demonstrated 90° scattering in U(2) soliton-antisoliton collisions.

Analyzed 60° scattering in complex soliton-antisoliton interactions.

Abstract

In this paper we study the noncommutative extension of a modified U(n) sigma model in 2+1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U(3) solitons and consider the head-on collision of a U(2) soliton and an antisoliton explicitly, which will result in a 90^{\text{o}} angle scattering. Further we discuss the head-on collision of one U(2) soliton with two antisolitons. This results in a 60^{\text{o}} angle scattering.