### 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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

}

*Communications in Mathematical Physics*, vol. 296, no. 2, pp. 323-351. https://doi.org/10.1007/s00220-010-1021-z

**Uniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two higgs particles.** / Chern, Jann Long; Chen, Zhi-You; Lin, Chang Shou.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two higgs particles

AU - Chern, Jann Long

AU - Chen, Zhi-You

AU - Lin, Chang Shou

PY - 2010/3/10

Y1 - 2010/3/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77952095556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952095556&partnerID=8YFLogxK

U2 - 10.1007/s00220-010-1021-z

DO - 10.1007/s00220-010-1021-z

M3 - Article

AN - SCOPUS:77952095556

VL - 296

SP - 323

EP - 351

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -