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Phase dynamics in the real Ginzburg-Landau equation

By Ian Melbourne and Guido Schneider

Abstract

<p>Spatially periodic equilibria <i>A</i>(<i>X</i>, <i>T</i>) = 1 - q2 eiqX+i0 are the locally preferred planform for the Ginzburg-Landau equation TA = 2XA + 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 q = 2h(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.</p

Year: 2004
DOI identifier: 10.1002/mana.200310129
OAI identifier: oai:epubs.surrey.ac.uk:1544

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