Existence Of Topological Solutions In A Maxwell--Chem--Simons Model

In this paper, we prove the existence of finite-energy topological solutions in a Maxwell-Chern-Simons model. We discuss the model with self-dual potential as well as the model with the non-self-dual potential. In the first case, we present several sharp existence and uniqueness theorems for the domain wall solutions of the basic govern-ing equations in1D, and we also show the equivalence of the BPS equations and the Euler-Lagrange equations and establish the properties of the domain wall solutions; In the second case, we prove the existence of finite-energy charged vortex solutions by a constrained minimization method applied on an indefinite action functional in2D, and we also show that the solution obtained is a classical solution.