Spectrum of the Linearized Operator for the Ginzburg-Landau Equation

Date

2000-06-09

Authors

Lin, Tai-Chia

Journal Title

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Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.

Description

Keywords

Ginzburg-Landau equation, Spectrum, Vortex dynamics, Superfluid

Citation

Lin, T. C. (2000). Spectrum of the linearized operator for the Ginzburg-Landau equation. <i>Electronic Journal of Differential Equations, 2000</i>(42), pp. 1-25.

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Attribution 4.0 International

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