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The Stability of Magnetic Vortices

S. Gustafson·I. M. Sigal
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Abstract

We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that the higher-degree vortices (|n| > 1) are stable for k < 1 and unstable for k > 1. This resolves a long-standing conjecture.

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S. Gustafson, I. M. Sigal. 1999-04-28. The Stability of Magnetic Vortices. https://arxiv.org/abs/math/9904158

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