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ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

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Abstract

We prove that a set ofN not necessarily distinct points in the plane determine a unique, real analytic solution to the first order Ginzburg-Landau equations with vortex numberN. This solution has the property that the Higgs field vanishes only at the points in the set and the order of vanishing at a given point is determined by the multiplicity of that point in the set. We prove further that these are the onlyC solutions to the first order Ginzburg-Landau equations.

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Communicated by A. Jaffe

This work is supported in part through funds provided under Contract PHY 77-18762

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Taubes, C.H. ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations. Commun.Math. Phys. 72, 277–292 (1980). https://doi.org/10.1007/BF01197552

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  • DOI: https://doi.org/10.1007/BF01197552

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