MOTION OF VORTEX LINES IN THE GINZBURG-LANDAU MODEL

Equations of motion for vortex lines in the Ginzburg-Landau theory are derived. We construct asymptotic approximations for the complex order parameter which are valid in the core region and in the far field. Using the method of matched asymptotic expansions we show that, to leading order, the line moves in the binormal direction with a curvature-dependent velocity. We also consider the contribution of remote parts of the line, interaction between several vortex lines and interaction with external fields.