We derive the exact equation of motion for a vortex in two- and three-dimensional nonrelativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the magnitude and phase of the complex field and is exact also for arbitrarily small intervortex distances. The results for vortices in a superfluid or a superconductor are recovered.
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Törnkvist et al. (1997) studied this question.
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