99-16 S. Gustafson, I.M. Sigal

The stability of magnetic vortices (72K, LaTeX) Jan 15, 99

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Abstract. We study the linearized stability of n-vortex (n an integer) 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, $\lambda$, and we prove that the higher-degree vortices (|n| $\geq$ 2) are stable for $\lambda < 1$ and unstable for $\lambda > 1$. This resolves a long-standing conjecture (see, eg, Jaffe-Taubes).

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