Application of the nonlinear Fourier transform for analysis of the coherent structures generation

The conventional (linear) Fourier transform represents a signal as a set of spectral harmonics, which helps in understanding its structure and properties. A related approach exists for certain classes of integrable nonlinear equations that can be solved via the inverse scattering transform, also known as the nonlinear Fourier transform (NFT). A particularly important example for optical applications is the nonlinear Schrödinger equation (NLSE), one of the fundamental equations of nonlinear science. This work applies the NFT to the analysis of how coherent structures are generated.

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@inproceedings{chekhovskoy2025application,
  title={Application of the nonlinear Fourier transform for analysis of the coherent structures generation},
  author={Chekhovskoy, IS and Shtyrina, OV and Fedoruk, MP and Sedov, EV and Turitsyn, SK},
  booktitle={2025 Conference on Lasers and Electro-Optics Europe \& European Quantum Electronics Conference (CLEO/Europe-EQEC)},
  year={2025},
  organization={IEEE},
  doi={10.1109/CLEO/Europe-EQEC65582.2025.11109113}
}