Effective dynamics of multi-vortices in an external potential for the Ginzburg–Landau gradient flow

We study the dynamics of multi-vortex configurations to the Ginzburg-Landau dissipative/gradient flow equations with external potential in ℝ². We show that for initial data close to the widely spaced multi-vortex configurations, the effective dynamics of the vortex centres are governed by the inter-vortex forces and by external potential forces for weak and strong external potentials, respectively. Copyright © 2010 IOP Publishing Ltd and London Mathematical Society.