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Zhiyou Chen · Jannlong Chern. Topological multivortex solutions for the Chern–Simons system with two Higgs particles. 2016.
An elliptic equation arising from the study o fstatic solutions with prescribed zeros and poles of the Einstein equations coupled with the classical sigma model and an Abelian gauge field, is considered. We classify the solutions and establish the uniqueness of radially symmetric solutions. We also complete a classification of symmetric solutions of an elliptic equation on the sphere.
The existence of topological solutions for the Chern-Simons equation with
two Higgs particles has been proved by Lin, Ponce and Yang . However, both the
uniqueness problem and the existence of non-topological solutions have been left open.
In this paper, we consider the case of one vortex at origin. Among others, we prove the
uniqueness of topological solutions and give a complete study of the radial solutions, in
particular, the existence of some non-topological solutions
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In this paper, we prove the uniqueness of topological multivortex solutions for the self-dual Maxwell–Chern–Simons U(1)U(1) model if the Chern–Simons coupling parameter is sufficiently large and the charge of electron is sufficiently small or large. On the other hand, we also establish the sharp region of the flux for non-topological solutions and provide the classification of radial solutions of all types in the case of one vortex point.