English

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