Noncommutative Solitons

TL;DR

This paper explores solitons in three-dimensional Moyal-deformed sigma models, focusing on their properties, interactions, and reductions, including integrable deformations of classical systems.

Contribution

It provides new insights into static and moving solitons in noncommutative sigma models, their scattering behavior, and stability, along with integrable deformations of classical equations.

Findings

Analysis of multi-soliton solutions in noncommutative settings

Characterization of soliton scattering and moduli space dynamics

Development of integrable deformations of classical models

Abstract

These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their scattering, moduli space dynamics, stability and dimensional reduction, including an integrable deformation of the sine-Gordon system.