# Existence theorems for non-Abelian Chern--Simons--Higgs vortices with flavor

@article{Chen2013ExistenceTF,
title={Existence theorems for non-Abelian Chern--Simons--Higgs vortices with flavor},
author={S. Chen and X. Han and G. Lozano and F. A.Schaposnik},
journal={arXiv: Analysis of PDEs},
year={2013}
}
In this paper we establish the existence of vortex solutions for a Chern--Simons--Higgs model with gauge group $SU(N) \times U(1)$ and flavor SU(N), these symmetries ensuring the existence of genuine non-Abelian vortices through a color-flavor locking. Under a suitable ansatz we reduce the problem to a $2\times 2$ system of nonlinear elliptic equations with exponential terms. We study this system over the full plane and over a doubly periodic domain, respectively. For the planar case we use a… Expand
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