Dynamic Stability and Instability of Pinned Fundamental Vortices

被引：7

作者：

Gustafson, S. ^{[2
]}

Ting, F. ^{[1
]}

机构：

[1] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

JOURNAL OF NONLINEAR SCIENCE | 2009年 / 19卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Ginzburg-Landau; External potential; Gradient and Hamiltonian dynamics; Orbital stability/instability; Pinned vortices; Asymptotic stability; NONLINEAR SCHRODINGER-EQUATIONS; SEMICLASSICAL BOUND-STATES; GINZBURG-LANDAU; SYMMETRIC VORTICES; MAGNETIC VORTICES; PINNING PHENOMENA; VORTEX; SUPERCONDUCTIVITY; POTENTIALS; EXISTENCE;

D O I：

10.1007/s00332-009-9039-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：341 / 374

页数：34

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