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> The non-linear Fourier transform (..) seems impressively obscure (I know of a total of one book reference)

Are those talking about the same thing?

[Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools](https://arxiv.org/abs/1202.3653)

[Nonlinear Fourier Analysis](https://arxiv.org/abs/1201.5129)




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