Uniqueness of the topological multivortex solution in the self-dual Chern–Simons theory

Abstract

We establish a uniqueness result for the topological multivortex solution to the self-dual equations of the Abelian relativistic self-dual Chern–Simons–Higgs model. We prove that the topological multivortex solution is unique if the Chern–Simons coupling parameter κ>0 is sufficiently small. We also establish a uniqueness result for κ>0 sufficiently large.