Abstract:
We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]).
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Received: 16 November 1998 / Accepted: 3 January 2000
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ID="*"Research on this paper was supported by NSERC under grant N7901
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ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.¶E-mail: gustaf@cims.nyu.edu
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GustafsonRID="**"ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.¶E-mail: gustaf@cims.nyu.edu, S., Sigal, I. The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901. Comm Math Phys 212, 257–275 (2000). https://doi.org/10.1007/PL00005526
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DOI: https://doi.org/10.1007/PL00005526