In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions in a 2 × 2 nonlinear elliptic system arising in the study of self-dual non-Abelian Chern-Simons vortices. We show that the system admits at least two solutions when the Chern-Simons coupling parameter ? >0 sufficiently large. As in Nolasco and Tarantello (Commun Math Phys 213:599-639, 2000), we use a variational formulation of the problem. Thus, we obtain a first solution via a constrained minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as ? ? 0. Then we obtain a second solution by a min-max procedure of "mountain pass" type.

Han, X., Tarantello, G. (2013). Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 49(3-4), 1149-1176 [10.1007/s00526-013-0615-7].

Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model

TARANTELLO, GABRIELLA
2013-01-01

Abstract

In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions in a 2 × 2 nonlinear elliptic system arising in the study of self-dual non-Abelian Chern-Simons vortices. We show that the system admits at least two solutions when the Chern-Simons coupling parameter ? >0 sufficiently large. As in Nolasco and Tarantello (Commun Math Phys 213:599-639, 2000), we use a variational formulation of the problem. Thus, we obtain a first solution via a constrained minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as ? ? 0. Then we obtain a second solution by a min-max procedure of "mountain pass" type.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Han, X., Tarantello, G. (2013). Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 49(3-4), 1149-1176 [10.1007/s00526-013-0615-7].
Han, X; Tarantello, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/90203
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