### Abstract

This paper presents a resolution of the gauged O(3) sigma model proposed by B.J. Schroers in which the matter field φ maps R^{2} into S^{2} while the vector gauge potential gives rise to a magnetic field. It is shown that for each natural number N there are solutions to saturate the classical energy lower bound E ≧ 4πN for the field configurations in the topological family deg(φ) = N if and only if N ≠ 1. Furthermore the solutions obtained depend on at least 4N - 3 continuous parameters, the associated magnetic flux can assume its value in an open interval, and the decay rates of the field strengths may be specified in a suitable range. These solutions are multisolitons represented by N prescribed lumps of the magnetic field, simulating N identical particles in equilibrium, and are governed by a nonlinear elliptic equation with both vortex and anti-vortex source terms.

Original language | English (US) |
---|---|

Pages (from-to) | 485-506 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 181 |

Issue number | 2 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

**A necessary and sufficient condition for the existence of multisolitons in a self-dual gauged sigma model.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 181, no. 2, pp. 485-506.

}

TY - JOUR

T1 - A necessary and sufficient condition for the existence of multisolitons in a self-dual gauged sigma model

AU - Yang, Yisong

PY - 1996

Y1 - 1996

N2 - This paper presents a resolution of the gauged O(3) sigma model proposed by B.J. Schroers in which the matter field φ maps R2 into S2 while the vector gauge potential gives rise to a magnetic field. It is shown that for each natural number N there are solutions to saturate the classical energy lower bound E ≧ 4πN for the field configurations in the topological family deg(φ) = N if and only if N ≠ 1. Furthermore the solutions obtained depend on at least 4N - 3 continuous parameters, the associated magnetic flux can assume its value in an open interval, and the decay rates of the field strengths may be specified in a suitable range. These solutions are multisolitons represented by N prescribed lumps of the magnetic field, simulating N identical particles in equilibrium, and are governed by a nonlinear elliptic equation with both vortex and anti-vortex source terms.

AB - This paper presents a resolution of the gauged O(3) sigma model proposed by B.J. Schroers in which the matter field φ maps R2 into S2 while the vector gauge potential gives rise to a magnetic field. It is shown that for each natural number N there are solutions to saturate the classical energy lower bound E ≧ 4πN for the field configurations in the topological family deg(φ) = N if and only if N ≠ 1. Furthermore the solutions obtained depend on at least 4N - 3 continuous parameters, the associated magnetic flux can assume its value in an open interval, and the decay rates of the field strengths may be specified in a suitable range. These solutions are multisolitons represented by N prescribed lumps of the magnetic field, simulating N identical particles in equilibrium, and are governed by a nonlinear elliptic equation with both vortex and anti-vortex source terms.

UR - http://www.scopus.com/inward/record.url?scp=0040201687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040201687&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040201687

VL - 181

SP - 485

EP - 506

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -