Phase dynamics in the real Ginzburg‐Landau equation

Spatially periodic equilibria A ( X, T ) = √1 − q 2 e   iqX + iϕ   0are 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)