The Ginzburg-Landau equation III. Vortex dynamics

Abstract

In this paper we study the time-dependent Ginzburg-Landau equation of the Schrödinger type in two dimensions. The initial conditions are chosen to describe several well-separated vortices. Our task is to understand the vortex structure of the corresponding solutions as well as corrections due to radiation. To this end we develop the nonlinear adiabatic theory. Using the methods of effective action and of geometric solvability we derive equations for the vortex dynamics and radiation. As an example we consider the special case of radiation by two 1-vortices.