Long-time behaviour of Ginzburg-Landau vortices

In this paper we continue our study of the long-time behaviour of solutions of the non-stationary Ginzburg Landau equation of the Schrödinger type. Here we consider initial conditions corresponding to either two vortices of charges +1 each or two vortices of opposite charges +1 and -1. We show that in the first case the vortices radiate while rotating around each other. As a result of this radiation they move apart at the rate of asymptotically. In the second case we show that the radiation is absent for large vortex separations which conforms with previous results. For separations of orders O (1) and less we argue that the vortex pair produces a shock wave. As a result it loses energy and eventually collapses.