Theoretical seminar | 25 June 2025

The report is devoted to the inverse scattering transform (IST) for the nonlinear Schrödinger equation (NLSE), often referred to in the literature as the Nonlinear Fourier Transform (NFT). The prospects for its use as a tool for compensating for nonlinear distortions in fiber-optic communication lines will be discussed and a comparison with some existing techniques will be made. In addition, various approaches to using NFT for laser radiation analysis will be discussed.

Main paper/arXiv, related to the seminar, and other references

[1] V. E. Zakharov and A. B. Shabat, “Exact Theory of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation of Waves in Non-Linear Media,” JETP 34, 62–69 (1972).
[2] I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk, S. B. Medvedev, and S. K. Turitsyn, “Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems,” Phys. Rev. Lett. 122, 153901 (2019)
[3] E. V. Sedov, I. S. Chekhovskoy, M. P. Fedoruk, and S. K. Turitsyn. Numerical Approaches in Nonlinear Fourier Transform-Based Signal Processing for Telecommunications. Studies in Applied Mathematics, 154(1), Article e12795 (2025).
[4] I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk, and S. K. Turitsyn, Inverse Scattering Transform: From Solving Equations to Facilitating Analysis Of Coherent Structures. http://dx.doi.org/10.2139/ssrn.5275921
[5] E. V. Sedov and I. S. Chekhovskoy, "Next-generation signal processing using windowed nonlinear Fourier transform", Proc. SPIE 13004, Nonlinear Optics and its Applications 2024, 130040Z (20 June 2024); https://doi.org/10.1117/12.3022429