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Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation

Published online by Cambridge University Press:  14 November 2011

Xinfu Chen ,
Charles M. Elliott  and
Tang Qi
Xinfu Chen
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
Charles M. Elliott
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9QH, U.K.
Tang Qi
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9QH, U.K.
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Abstract

In this paper, we study all the stationary solutions of the form u(r)einθ to the complex-valued Ginzburg–Landau equation on the complex plane: here (r, θ) are the polar coordinates, and n is any real number. In particular, we show that there exists a unique solution which approaches to a nonzero constant as r → ∞.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1075 - 1088
Copyright
Copyright © Royal Society of Edinburgh 1994

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