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Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons System with Two Higgs Particles

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Abstract

The existence of topological solutions for the Chern-Simons equation with two Higgs particles has been proved by Lin, Ponce and Yang [16]. However, both the uniqueness problem and the existence of non-topological solutions have been left open. In this paper, we consider the case of one vortex at origin. Among others, we prove the uniqueness of topological solutions and give a complete study of the radial solutions, in particular, the existence of some non-topological solutions.

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Authors and Affiliations

  1. Department of Mathematics, National Central University, Chung-Li, 32001, Taiwan

    Jann-Long Chern & Zhi-You Chen

  2. Department of Mathematics, Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan

    Chang-Shou Lin

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  1. Jann-Long Chern
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  2. Zhi-You Chen
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  3. Chang-Shou Lin
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Correspondence to Jann-Long Chern.

Additional information

Communicated by M. Aizenman

Work partially supported by National Science Council of Taiwan.

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Chern, JL., Chen, ZY. & Lin, CS. Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons System with Two Higgs Particles. Commun. Math. Phys. 296, 323–351 (2010). https://doi.org/10.1007/s00220-010-1021-z

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