2012/09/17 by Xiaosen Han, Han, Xiaosen, Gabriella Tarantello +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1209.3535
arxiv created 2012/09/17 · openalex publication_date 2012/09/17 · arxiv updated 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions for a 2×2 nonlinear elliptic system arising in the study of self-dual non-Abelian Chern--Simons vortices. We show that the given system admits at least two solutions when the Chern--Simons coupling parameter κ>0 is sufficiently small; while no solutions exist for κ>0 sufficiently large. As in [36] we use a variational formulation of the problem. Thus, we obtain a first solution via a (local) minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as κ→ 0. Then we obtain the second solution by a min-max procedure of "mountain pass" type.