Reconnection of Vortex Filaments in the Complex Ginzburg-Landau Equation

A criterion for the reconnection of vortex filaments in the complex Ginzburg-Landau equation is presented. In particular, we give an estimate of the maximum intervortex separation beyond which coplanar filaments of locally opposite charge will not reconnect. This is done by balancing the motion of the filaments toward each other that would result if they were straight (a two-dimensional effect) with the opposing motion due to the filament curvature. Numerical experiments are in good agreement with the estimated vortex separation.