The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the reduced dynamic laws. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex interactions in the GLSE. Finally, the vortex motion under an inhomogeneous potential in the GLSE is also studied.


Mathematics and Statistics

Keywords and Phrases

Ginzburg-Landau equation; nonlinear Schrodinger equation; complex Ginzburg-Landau equation; Ginzburg-Landau-Schrodinger equation; vortex state; reduced dynamic laws; vortex interaction

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

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© 2007 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.

Publication Date

01 Jan 2007