Bulletin of the
Korean Mathematical Society
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ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(3): 765-777

Printed May 31, 2016

https://doi.org/10.4134/BKMS.b150302

Copyright © The Korean Mathematical Society.

Remarks on nontopological solutions in the self-dual Chern-Simons gauged $O(3)$ sigma models

Nari Choi and Jongmin Han

Kyung Hee University, Kyung Hee University

Abstract

In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged $O(3)$ sigma models. The property of solutions depends on a parameter $\tau \in [-1,1]$ appearing in the nonlinear term. The case $\tau=1$ lies on the borderline for the existence of solutions in the previous results \cite{CH13R2, CH11, CHLLi}. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1\le \tau<1$, we establish solutions which are perturbed from the solutions of singular Liouville equations.

Keywords: Chern-Simons gauged $O(3)$ sigma model, nontopological solu\-tions

MSC numbers: Primary 81T13, 35B40

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