TOPOLOGICAL MULTIVORTEX SOLUTIONS OF THE SELF-DUAL MAXWELL-CHERN-SIMONS-HIGGS SYSTEM

We study the existence and various behaviors of topological multivorte x solutions of the relativistic self-dual Maxwell-Chern-Simons-Higgs s ystem. We first prove the existence of general topological solutions b y applying variational methods to the newly discovered minimizing func tional. Then, by an iteration method, we prove the existence of topolo gical solutions satisfying some extra conditions, which we call admiss ible solutions. We establish asymptotic exponential decay estimates fo r these topological solutions. We also investigate the limiting behavi or of the admissible solutions as parameters rn our system go to some limits. For the Abelian Higgs limit we obtain strong convergence resul t, while for the Chern-Simons limit we only obtained that our admissib le solutions weakly approximate one of the Chern-Simons solutions. (C) 1997 Academic Press.