Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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REMARKS ON NONTOPOLOGICAL SOLUTIONS IN THE SELF-DUAL CHERN-SIMONS GAUGED O(3) SIGMA MODELS

  • Choi, Nari (Department of Mathematics Kyung Hee University) ;
  • Han, Jongmin (Department of Mathematics Kyung Hee University)
  • Received : 2015.04.29
  • Published : 2016.05.31
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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 [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1{\leq}{\tau}$<1, we establish solutions which are perturbed from the solutions of singular Liouville equations.

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References

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