Dynamic stability and instability of pinned fundamental vortices

S. Gustafson, F. Ting

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

We study the dynamic stability and instability of pinned fundamental ±1 vortex solutions to the Ginzburg-Landau equations with external potential in ℝ 2. For sufficiently small external potentials, there exists a perturbed vortex solution centered near each non-degenerate critical point of the potential. With respect to both dissipative and Hamiltonian dynamics, we show that perturbed vortex solutions which are concentrated near local maxima (resp. minima) are orbitally stable (resp. unstable). In the dissipative case, the stability is in the stronger "asymptotic" sense.

Original languageEnglish
Pages (from-to)341-374
Number of pages34
JournalJournal of Nonlinear Science
Volume19
Issue number4
DOIs
Publication statusPublished - Aug 2009
Externally publishedYes

Keywords

  • Asymptotic stability
  • External potential
  • Ginzburg-Landau
  • Gradient and Hamiltonian dynamics
  • Orbital stability/instability
  • Pinned vortices

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

Cite this