Nontopological solutions in the self-dual Maxwell–Chern–Simons gauged O(3) sigma model. (May 2015)

• Record Type: Journal Article
• Authors: Han, Jongmin; Song, Kyungwoo
• Is Part Of: Nonlinear analysis. Volume 118(2015)
• Page Start: 22
• Page End: 40
• Publication Date: 2015-05
• Subjects: Self-dual Maxwell–Chern–Simons gauged O(3) sigma model -- Nontopological solutions -- Generalized implicit function theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.01.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove the existence of nontopological solutions in the self-dual Maxwell–Chern–Simons gauged O ( 3 ) sigma model in the plane. If the scaling parameter is small enough, the reduced equation can be regarded as a perturbation of the Liouville equation. Then, we use the Generalized Implicit Function Theorem to prove the existence of solutions with nontopological boundary conditions. Using this result, we show the existence of symmetrically topological solutions and nontopological solutions for the original self-dual equations whose magnetic fluxes are slightly bigger than the critical value. Moreover, we also compute the topological charge and the degree of the spin vectors.