### Abstract

We study the r × r system of nonlinear elliptic equations (formula presented) where λ > O is a constant parameter, K - (K_{ab}) is the Cartan matrix of a semi-simple Lie algebra, and op is the Dirac measure concentrated at p ∈ R^{2}. This system of equations arises in the relativistic non-Abelian Chern-Simons theory and may be viewed as a non-integrable deformation of the integrable Toda system. We establish the existence of a class of solutions known as topological multivortices. The crucial step in our method is the use of the decomposition theorem of Cholesky for positive definite matrices so that a variational principle can be formulated.

Original language | English (US) |
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Pages (from-to) | 199-218 |

Number of pages | 20 |

Journal | Communications In Mathematical Physics |

Volume | 186 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1997 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics