We study the vortex trajectories for the two-dimensional complex parabolic Ginzburg-Landau equation without a well-preparedness assumption. We prove that the trajectory set is rectifiable, and satisfies a weak motion law. In the case of degree ± 1 vortices, the motion law is satisfied in the classical sense. Moreover, dissipation occurs only at a finite number of times. Away from these times, possible collisions and splittings of vortices are constrained by algebraic equations involving their topological degrees
Quantization and motion law for Ginzburg-Landau vortices
ORLANDI, Giandomenico;
2007-01-01
Abstract
We study the vortex trajectories for the two-dimensional complex parabolic Ginzburg-Landau equation without a well-preparedness assumption. We prove that the trajectory set is rectifiable, and satisfies a weak motion law. In the case of degree ± 1 vortices, the motion law is satisfied in the classical sense. Moreover, dissipation occurs only at a finite number of times. Away from these times, possible collisions and splittings of vortices are constrained by algebraic equations involving their topological degrees
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