Spectrum of the Linearized Operator for the Ginzburg-Landau Equation
Date
2000-06-09
Authors
Lin, Tai-Chia
Journal Title
Journal ISSN
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.
Rights
Attribution 4.0 International