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INSTABILITY OF SPATIALLY QUASI-PERIODIC STATES OF THE GINZBURG-LANDAU EQUATION
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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 | ||||
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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 | ||||
Official Date: | 8 February 1994 | ||||
Dates: |
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Volume: | 444 | ||||
Number: | 1921 | ||||
Number of Pages: | 16 | ||||
Page Range: | pp. 347-362 | ||||
Publication Status: | Published |
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