Abstract:
We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 16 November 1998 / Accepted: 3 January 2000
RID="*"
ID="*"Research on this paper was supported by NSERC under grant N7901
RID="**"
ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.¶E-mail: gustaf@cims.nyu.edu
Rights and permissions
About this article
Cite this article
GustafsonRID="**"ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.¶E-mail: gustaf@cims.nyu.edu, S., Sigal, I. The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901. Comm Math Phys 212, 257–275 (2000). https://doi.org/10.1007/PL00005526
Issue Date:
DOI: https://doi.org/10.1007/PL00005526