### 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.

Original language | English |
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Pages (from-to) | 323-351 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 296 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2010 Mar 10 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Chern, J. L., Chen, Z-Y., & Lin, C. S. (2010). Uniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two higgs particles.

*Communications in Mathematical Physics*,*296*(2), 323-351. https://doi.org/10.1007/s00220-010-1021-z