Existence and Asymptotics for the Topological Chern-Simons Vortices of the $CP(1)$ Model
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In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in R2. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern- Simons coupling constant goes to zero and the convergence is exponentially fast.
Abstract
In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in R2. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern- Simons coupling constant goes to zero and the convergence is exponentially fast.
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