### 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) |
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Pages (from-to) | 573-585 |

Number of pages | 13 |

Journal | Helvetica Physica Acta |

Volume | 71 |

Issue number | 5 |

State | Published - Oct 1998 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Yang, Y. (1998). Chern-Simons solitons and a nonlinear elliptic equation.

*Helvetica Physica Acta*,*71*(5), 573-585.