Topological solutions in the Maxwell-Chern-Simons model with anomalous magnetic moment
Youngae Lee
Discrete & Continuous Dynamical Systems - A 2018, 38(3): 1293-1314 doi: 10.3934/dcds.2018053

In this paper, we consider a Maxwell-Chern-Simons model with anomalous magnetic moment. Our main goal is to show the existence and uniqueness of topological type solutions to this problem on a flat two torus for any configuration of vortex points. Moreover, we also discuss about the stability of topological solutions.

keywords: Maxwell-Chern-Simons models topological type solutions stable solution uniqueness
Non-topological solutions in a generalized Chern-Simons model on torus
Youngae Lee
Communications on Pure & Applied Analysis 2017, 16(4): 1315-1330 doi: 10.3934/cpaa.2017064

We consider a quasi-linear elliptic equation with Dirac source terms arising in a generalized self-dual Chern-Simons-Higgs gauge theory. In this paper, we study doubly periodic vortices with arbitrary vortex configuration. First of all, we show that under doubly periodic condition, there are only two types of solutions, topological and non-topological solutions as the coupling parameter goes to zero. Moreover, we succeed to construct non-topological solution with $k$ bubbles where $k\in\mathbb{N}$ is any given number. To find a solution, we analyze the structure of quasi-linear elliptic equation carefully and apply the method developed in the recent work [16].

keywords: Generalized self-dual Chern-Simons model doubly periodic vortices bubbling non-topological solution

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