Soliton Scattering in Noncommutative Spaces

TL;DR

This paper presents exact multi-soliton solutions in noncommutative spaces, showing that soliton scattering behaviors mirror those in commutative spaces, with preserved shapes, velocities, and phase shifts, and introduces solutions to noncommutative Yang-Mills hierarchies.

Contribution

It provides new multi-soliton solutions in noncommutative integrable systems and analyzes their scattering, including detailed 2-soliton interactions in noncommutative Yang-Mills hierarchies.

Findings

Soliton configurations in noncommutative spaces resemble commutative ones.

Soliton shape, velocity, and phase shifts are preserved during scattering.

New multi-soliton solutions to noncommutative anti-self-dual Yang-Mills hierarchy are presented.

Abstract

We discuss exact multi-soliton solutions to integrable hierarchies on noncommutative space-times in diverse dimension. The solutions are represented by quasi-determinants in compact forms. We study soliton scattering processes in the asymptotic region where the configurations could be real-valued. We find that the asymptotic configurations in the soliton scatterings can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized lump of energy and each solitary wave-packet lump preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. As new results, we present multi-soliton solutions to noncommutative anti-self-dual Yang-Mills hierarchy and discuss 2-soliton scattering in detail.