Multiple Vortices In The Magnetic Impurities Model

We describe the BPS dynamics of vortices in the presence of impurities. In this paper, we present a series of existence and uniqueness theorems for multiple vortex solutions of the magnetic impurities model over R2 and on a doubly periodic domain. Our methods are based on calculus of variations and a fixed-point argument. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are expressed in terms of several physical parameters involved explicitly.