Dynamic stability and instability of pinned fundamental vortices

We study the dynamic stability and instability of pinned fundamental ±1 vortex solutions to the Ginzburg-Landau equations with external potential in ℝ². 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. Copyright © 2009 Springer Science+Business Media, LLC.