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[SOLVED] Fast Fourier Transform and its inverse

dwsmith

Well-known member
Feb 1, 2012
1,673
Does every FFT have \(i\) in it?

Given \(u_t = -(u_{xxx} + 6uu_x)\).

\(f'''(x) = \mathcal{F}^{-1}\left[(ik)^3\mathcal{F}(f(x))\right]\)
\(f'(x) = \mathcal{F}^{-1}\left[(ik)\mathcal{F}(f(x))\right]\)

The only equation I have used the pseudo-spectral method on was the NLS which is
\(u_t = i(u_{xx} + |u|^2u)\). In this case, I know I will have \(i\) in the FFT.

Are my transforms for the KdV correct or do I need to remove \(i\)?