Topological Multivortex Solutions of the Self-Dual Maxwell-Chern-Simons-Higgs System

TL;DR

This paper investigates the existence, behavior, and limits of topological multivortex solutions in a self-dual Maxwell-Chern-Simons-Higgs system, using variational and iterative methods to establish decay estimates and convergence properties.

Contribution

It introduces new methods to prove the existence of topological solutions and analyzes their asymptotic behaviors and limits within the system.

Findings

Existence of general topological solutions proved via variational methods.

Asymptotic exponential decay estimates established for solutions.

Convergence results obtained in the Abelian Higgs and Chern-Simons limits.

Abstract

We study existence and various behaviors of topological multivortices solutions of the relativistic self-dual Maxwell-Chern-Simons-Higgs system. We first prove existence of general topological solutions by applying variational methods to the newly discovered minimizing functional. Then, by an iteration method we prove existence of topological solutions satisfying some extra conditions, which we call admissible solutions. We establish asymptotic exponential decay estimates for these topological solutions. We also investigate the limiting behaviors of the admissible solutions as parameters in our system goes to some limits. For the Abelian Higgs limit we obtain strong convergence result, while for the Chern-Simons limit we only obtained that our admissible solutions are weakly approximating one of the Chern-Simons solutions.