UNSPECIFIED (1994) INSTABILITY OF SPATIALLY QUASI-PERIODIC STATES OF THE GINZBURG-LANDAU EQUATION. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 444 (1921). pp. 347-362. ISSN 1364-5021

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Abstract

The Ginzburg-Landau (GL) equation with real coefficients is a model equation appearing in superconductor physics and near-critical hydrodynamic stability problems. The stationary GL equation has a two-parameter (I-1,I-2) family of spatially quasi-periodic (QP) states with frequencies (omega(1) omega(2)) and frequency map with determinant Delta(K) = partial derivative(omega(1),omega(2))/partial derivative(I-1,I-2) In this paper the linear stability of these QP states is studied and an expression for the stability exponent is obtained which has a novel geometric interpretation in terms of Delta(K): when Delta(K) < 0 the spatially QP state is unstable and Delta(K) > 0 is a necessary but not sufficient condition for linear stability. There is an interesting relation between Delta(K) and the KAM persistence theorem for invariant toroids.

Item Type:	Journal Article
Subjects:	Q Science
Journal or Publication Title:	PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Publisher:	ROYAL SOC LONDON
ISSN:	1364-5021
Date:	8 February 1994
Volume:	444
Number:	1921
Number of Pages:	16
Page Range:	pp. 347-362
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20825

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