[SOLVED] Amath 568 homework 7

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.