### 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) |
---|---|

Pages (from-to) | 199-218 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 186 |

Issue number | 1 |

State | Published - 1997 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*186*(1), 199-218.

**The relativistic non-Abelian Chern-Simons equations.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 186, no. 1, pp. 199-218.

}

TY - JOUR

T1 - The relativistic non-Abelian Chern-Simons equations

AU - Yang, Yisong

PY - 1997

Y1 - 1997

N2 - We study the r × r system of nonlinear elliptic equations (formula presented) where λ > O is a constant parameter, K - (Kab) is the Cartan matrix of a semi-simple Lie algebra, and op is the Dirac measure concentrated at p ∈ R2. 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.

AB - We study the r × r system of nonlinear elliptic equations (formula presented) where λ > O is a constant parameter, K - (Kab) is the Cartan matrix of a semi-simple Lie algebra, and op is the Dirac measure concentrated at p ∈ R2. 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.

UR - http://www.scopus.com/inward/record.url?scp=0031523741&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031523741&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031523741

VL - 186

SP - 199

EP - 218

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -