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[SOLVED] Amath 568 homework 7

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1. Consider the Optical Parametric Oscillator as given in Lecture 23 of the notes (Pages 99-102)
(a) Assuming slow time τ =
2
t and slow space ξ = x, derive the Fisher-Kolmogorov equation for
the slow evolution of the instability (the expression after Eq. (518))
(b) Derive the Swift-Hohenberg type expression which is governed by Eq. (519) with the scalings
detailed in the notes.