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
2007
Ginzburg-Landau; parabolic equations; vortex dynamics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/29006
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