Kwangseok Choe

Asymptotic behavior of condensate solutions in the Chern-Simons-Higgs theory

We study the asymptotic behavior of condensate solutions in the Chern-Simons-Higgs model as the Chern-Simons coupling parameter tends to zero. Using the variational method, we prove that there exist condensate solutions which show concentration phenomena.

Multiple Existence Results for the Self-Dual Chern–Simons–Higgs Vortex Equation

We study the asymptotic behavior for the condensate solutions of the self-dual Chern–Simons–Higgs equation as the Chern–Simons parameter tends to zero. By using these estimates, we establish existence results for solutions of non-topological type.

Existence and properties of radial solutions in the self-dual Chern-Simons O(3) sigma model

In this paper, we study the self-dual equations arising from the Chern-Simons gauged O(3) sigma model with symmetric potential. We prove the existence of radially symmetric solutions of the reduced elliptic equation having topological and nontopological boundary conditions.

Existence of mixed type solutions in the Chern–Simons gauge theory of rank two in R2

Abstract We consider the self-dual equations arising from the Chern–Simons gauge theory of rank 2 such as the S U ( 3 ) , S O ( 5 ) , and G 2 Chern–Simons model in R 2 . There are three possible types of solutions in these theories, namely, topological, nontopological, and mixed type solutions. The existence of a mixed type solution for an arbitrary configuration of vortex points has been a long-standing open problem. We construct here a family of mixed type solutions ( u 1 , e , u 2 , e ) , e > 0 for an arbitrary configuration of vortex points under a mild non-degeneracy condition. The main new idea of our construction of an approximate solution is to use different scalings for different components. In the process of the finite dimensional reduction, all estimates for this particular construction become rather delicate.