INSTABILITY OF SPATIALLY QUASI-PERIODIC STATES OF THE GINZBURG-LANDAU EQUATION
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 1364-5021Full text not available from this repository.
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|
|Journal or Publication Title:||PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES|
|Publisher:||ROYAL SOC LONDON|
|Official Date:||8 February 1994|
|Number of Pages:||16|
|Page Range:||pp. 347-362|
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