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On the Validity of the degenerate Ginzburg—Landau equation
Author(s) -
Shepeleva A.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970925)20:14<1239::aid-mma917>3.0.co;2-o
Subject(s) - mathematics , degenerate energy levels , dimension (graph theory) , nonlinear system , mathematical analysis , bifurcation , bifurcation theory , mathematical physics , pure mathematics , physics , quantum mechanics
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. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.