S. Gustafson, I.M. Sigal
The stability of magnetic vortices
(72K, LaTeX)

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).