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### INSTABILITY OF SPATIALLY QUASI-PERIODIC STATES OF THE GINZBURG-LANDAU EQUATION

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(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 |

Data sourced from Thomson Reuters' Web of Knowledge

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