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On the Validity of the degenerate Ginzburg—Landau equation

✍ Scribed by A. Shepeleva

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
159 KB
Volume
20
Category
Article
ISSN
0170-4214

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✦ Synopsis

The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem.

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