Dynamic stability and instability of pinned fundamental vortices

S. Gustafson; F. Ting

doi:10.1007/s00332-009-9039-0

Dynamic stability and instability of pinned fundamental vortices

S. Gustafson, F. Ting

Research output: Journal article publication › Journal article › Academic research › peer-review

10 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 language	English
Pages (from-to)	341-374
Number of pages	34
Journal	Journal of Nonlinear Science
Volume	19
Issue number	4
DOIs	https://doi.org/10.1007/s00332-009-9039-0
Publication status	Published - Aug 2009
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Modelling and Simulation
General Engineering
Applied Mathematics

More information

10.1007/s00332-009-9039-0

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AU - Ting, F.

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N2 - 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.

AB - 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.

KW - Asymptotic stability

KW - External potential

KW - Ginzburg-Landau

KW - Gradient and Hamiltonian dynamics

KW - Orbital stability/instability

KW - Pinned vortices

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DO - 10.1007/s00332-009-9039-0

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SN - 0938-8974

VL - 19

SP - 341

EP - 374

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 4

ER -

Dynamic stability and instability of pinned fundamental vortices

Abstract

Keywords

ASJC Scopus subject areas

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