### Abstract

We prove an existence theorem for the following quasilinear elliptic equation (1 - e^{u})Δu = |∇u|^{2}e^{u} - λ(1 - e^{u})^{2}e^{u} + 4πΣ_{j=1}^{N}δ_{pj} over the full plane subject to the boundary condition that u → 0 as |x| → ∞, where λ > 0 is a physical parameter and δ is the Dirac distribution concentrated at the point p. The solutions of the equation are vortex-like multi-solitons arising in a unified relativistic self-dual Chern-Simons theory.

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

Pages (from-to) | 573-585 |

Number of pages | 13 |

Journal | Helvetica Physica Acta |

Volume | 71 |

Issue number | 5 |

State | Published - Oct 1998 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Helvetica Physica Acta*,

*71*(5), 573-585.

**Chern-Simons solitons and a nonlinear elliptic equation.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Helvetica Physica Acta*, vol. 71, no. 5, pp. 573-585.

}

TY - JOUR

T1 - Chern-Simons solitons and a nonlinear elliptic equation

AU - Yang, Yisong

PY - 1998/10

Y1 - 1998/10

N2 - We prove an existence theorem for the following quasilinear elliptic equation (1 - eu)Δu = |∇u|2eu - λ(1 - eu)2eu + 4πΣj=1Nδpj over the full plane subject to the boundary condition that u → 0 as |x| → ∞, where λ > 0 is a physical parameter and δ is the Dirac distribution concentrated at the point p. The solutions of the equation are vortex-like multi-solitons arising in a unified relativistic self-dual Chern-Simons theory.

AB - We prove an existence theorem for the following quasilinear elliptic equation (1 - eu)Δu = |∇u|2eu - λ(1 - eu)2eu + 4πΣj=1Nδpj over the full plane subject to the boundary condition that u → 0 as |x| → ∞, where λ > 0 is a physical parameter and δ is the Dirac distribution concentrated at the point p. The solutions of the equation are vortex-like multi-solitons arising in a unified relativistic self-dual Chern-Simons theory.

UR - http://www.scopus.com/inward/record.url?scp=0038157705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038157705&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0038157705

VL - 71

SP - 573

EP - 585

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -