The Stability of Magnetic Vortices
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/9904158,
title = {The Stability of Magnetic Vortices},
author = {S. Gustafson and I. M. Sigal},
journal= {arXiv preprint arXiv:math/9904158},
year = {2007}
}
Comments
28 pages, Latex