Existence and uniqueness of topological multivortex solutions of the self-dual Chern–Simons image model Original Research Article

In this paper we study the existence and uniqueness of the topological Chern–Simons vortices in the View the MathML sourceCP(1) model in R2R2. 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.