So I just completed an undergraduate course on PDEs, and one of the ways(my personal favorite from the course) to solve a PDE is using Fourier Transforms. Fourier Transforms are linear transformations, but out of curiosity does there a exist a non-linear version or generalization of Fourier Transforms? Where this thought comes from is that I have worked with Euclidean Transformations which are linear until you generalize it to include translations at which point it becomes an affine(and therefore non-linear) transformation. I am curious to know if there was something similar for Fourier Transforms.
2026-05-05 06:12:54.1777961574
Does there exist a non-linear version of Fourier Transforms?
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