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- W4382601887 abstract "In Chapter 12 we saw how to derive amplitude equations from the Swift-Hohenberg equation. Here we provide a proof of our formal approximations. As before, we consider as a starting point the Swift-Hohenberg equationwhere p ∈ ℝ is a parameter and u(x,t) for x ∈ ℝ; observe that we restrict our attention here to the one-dimensional case to simplify the exposition. For the scalingsand the formal ansatzwe already know from Chapter 12 that the amplitude A = A(X, T) is expected to satisfy the (real) Ginzburg-Landau equation" @default.
- W4382601887 created "2023-06-30" @default.
- W4382601887 date "2019-01-01" @default.
- W4382601887 modified "2023-09-24" @default.
- W4382601887 title "Chapter 13: Validity of Amplitude Equations" @default.
- W4382601887 doi "https://doi.org/10.1137/1.9781611975666.ch13" @default.
- W4382601887 hasPublicationYear "2019" @default.
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