Noncommutative Multi-Solitons in 2+1 Dimensions

TL;DR

This paper constructs explicit multi-soliton solutions in a noncommutative 2+1 dimensional integrable U(n) sigma model, revealing their dynamics, scattering behavior, and asymptotic properties.

Contribution

It introduces a method to generate exact multi-soliton configurations in a noncommutative integrable field theory using the dressing method.

Findings

Explicit multi-soliton solutions with time dependence

Solutions exhibit finite energy lumps in motion

Proven asymptotic factorization at large times

Abstract

The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing method to construct explicit multi-soliton configurations on noncommutative R^{2,1}. These solutions, abelian and nonabelian, feature exact time-dependence for any value of the noncommutativity parameter theta and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.