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Phase dynamics in the real Ginzburg-Landau equation

✍ Scribed by Ian Melbourne; Guido Schneider

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
173 KB
Volume
263-264
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Spatially periodic equilibria A(X, T) = √1 − q^2^ e are the locally preferred planform for the Ginzburg‐Landau equation ∂~T~A = ∂^2^~X~A + A − A|A|^2^. To describe the global spatial behavior, an evolution equation for the local wave number q can be derived formally. The local wave number q satisfies approximately a so called phase diffusion equation ∂~τ~q = ∂^2^~ξ~h(q). It is the purpose of this paper to explain the extent to which the phase diffusion equation is valid by proving estimates for this formal approximation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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