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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.12 No.3

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Existence and Asymptotics for the Topological Chern-Simons Vortices of the $CP(1)$ Model

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2005, v.12 no.3, pp.169-178
NAM HEE-SEOK
NAM, H. (2005). Existence and Asymptotics for the Topological Chern-Simons Vortices of the $CP(1)$ Model. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 12(3), 169-178.

Abstract

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in <TEX>$\mathbb{R}^2$</TEX>. 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 Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

keywords
self-dual Chern-Simons CP(1) model, topological solution, local uniform convergence

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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