Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Instabilities of the Ginzburg-Landau equation: periodic solutions

Authors: Paul K. Newton and Lawrence Sirovich
Journal: Quart. Appl. Math. 44 (1986), 49-58
MSC: Primary 35Q20; Secondary 58F21
DOI: https://doi.org/10.1090/qam/840442
MathSciNet review: 840442
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Abstract: The evolution of spatially periodic unstable solutions to the Ginzburg-Landau equation is considered. These solutions are shown to remain pointwise bounded (Lagrange stable). The first step in the route to chaos is limit cycle behavior. This is treated by perturbation theory and shown to result in a factorable form. Agreement between the perturbation result and an exact numerical integration is shown to be excellent.

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DOI: https://doi.org/10.1090/qam/840442
Article copyright: © Copyright 1986 American Mathematical Society

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