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

We study the existence and various behaviors of topological multivortex solutions of the relativistic self-dual Maxwell–Chern–Simons–Higgs system. We first prove the existence of general topological solutions by applying variational methods to the newly discovered minimizing functional. Then, by an iteration method, we prove the 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 behavior of the admissible solutions as parameters in our system go 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 weakly approximate one of the Chern–Simons solutions.