Self-dual Chern-Simons solitons in noncommutative space

TL;DR

This paper constructs exact vortex-like soliton solutions in noncommutative Chern-Simons-Higgs models, demonstrating their smooth transition to known solutions as the noncommutative parameter approaches zero.

Contribution

It provides explicit solutions for both non-relativistic and relativistic models in noncommutative space, extending the understanding of Chern-Simons solitons.

Findings

Exact vortex-like solutions in noncommutative space

Solutions reduce to known solitons as noncommutative parameter approaches zero

Regular solutions to BPS equations in both models

Abstract

We construct exact soliton solutions to the Chern-Simons-Higgs system in noncommutative space, for non-relativistic and relativistic models. In both cases we find regular vortex-like solutions to the BPS equations which approach the ordinary selfdual non-topological and topological solitons when the noncommutative parameter $\theta$ goes to zero.