Pinning of magnetic vortices subject to multi-well potential in the Ginzburg-Landau theory of superconductivity
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I will study the existence of multi-vortex solutions of the Ginzburg-Landau equations with an external potential on R2. These equations model the equilibrium states of superconductors: the external potential, W, represents doped impurities or defects of the superconductor. I will show that if the critical points of the potential are spaced widely enough and if the potential W is "strong enough", then there exists a multi-vortex (perturbed) solution with each vortex centered near each critical point of W.