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Instability of quasiperiodic solutions of the Ginzburg–Landau equation

Published online by Cambridge University Press:  14 November 2011

A. Doelman ,
R. A. Gardner  and
C. K. R. T. Jones
A. Doelman
Affiliation:
Mathematisch Instituute, Rijksuniversiteit Utrecht, 3508 TA Utrecht, The Netherlands
R. A. Gardner
Affiliation:
Mathematics Department, University of Massachusetts, Amherst, MA 01003, U.S.A.
C. K. R. T. Jones
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI, U.S.A.
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Extract

In this paper we show that each quasiperiodic standing wave solution of the real Ginzburg–Landau equation which is on the global branch emanating from the Eckhaus unstable periodic orbit is itself unstable. A rigorous proof of the instability is given by showing that the linearised operator about such a solution has spectrum which contains an interval along the unstable axis of the spectral plane. The proof employs some geometric and topological methods arising from a dynamical systems approach to the analysis of the eigenvalue problem for the linearised operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 3 , 1995 , pp. 501 - 517
Copyright
Copyright © Royal Society of Edinburgh 1995

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