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Multi-Vortex Solutions to Ginzburg–Landau Equations with External Potential

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Abstract

We consider the existence of multi-vortex solutions to the Ginzburg–Landau equations with external potential on \({\mathbb{R}^2}\) . These equations model equilibrium states of superconductors and stationary states of the U(1) Higgs model of particle physics. In the former case, the external potential models impurities and defects. We show that if the external potential is small enough and the magnetic vortices are widely spaced, then one can pin one or an arbitrary number of vortices in the vicinity of a critical point of the potential. In addition, one can pin an arbitrary number of vortices near infinity if the potential is radially symmetric and of an algebraic order near infinity.

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Authors and Affiliations

  1. Department of Physics, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    A. Pakylak

  2. Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    F. Ting

  3. Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    J. Wei

Authors
  1. A. Pakylak
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  2. F. Ting
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  3. J. Wei
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Correspondence to F. Ting.

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Communicated by P. Rabinowitz

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Pakylak, A., Ting, F. & Wei, J. Multi-Vortex Solutions to Ginzburg–Landau Equations with External Potential. Arch Rational Mech Anal 204, 313–354 (2012). https://doi.org/10.1007/s00205-011-0478-z

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  • DOI: https://doi.org/10.1007/s00205-011-0478-z

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