Existence and uniqueness of topological multivortex solutions of the self-dual Chern–Simons [formula omitted] model

Abstract

In this paper we study the existence and uniqueness of the topological Chern–Simons vortices in the CP ( 1 ) model in R 2 . After reducing the self-dual equations to semilinear elliptic partial differential equations, we show that a topological solution exists, and it is unique up to a real smooth function if the Chern–Simons coupling constant is sufficiently small.