Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
Application of the nonlinear Fourier transform for analysis of the coherent structures generation. / Chekhovskoy, I. S.; Shtyrina, O. V.; Fedoruk, M. P. et al.
2025 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2025. Institute of Electrical and Electronics Engineers Inc., 2025. (2025 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2025).Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
}
TY - CHAP
T1 - Application of the nonlinear Fourier transform for analysis of the coherent structures generation
AU - Chekhovskoy, I. S.
AU - Shtyrina, O. V.
AU - Fedoruk, M. P.
AU - Sedov, E. V.
AU - Turitsyn, S. K.
PY - 2025
Y1 - 2025
N2 - The conventional (linear) Fourier transform is a widely used mathematical method in science and engineering. It allows the signal of interest to be represented as a set of spectral harmonics, which, in many situations, helps in understanding the structure and properties of that signal. In certain linear equations, where the spectral harmonics evolve independently, the Fourier transform provides a straightforward description of complex temporal or spatial dynamics. A related approach exists for certain classes of integrable nonlinear equations that can be solved via the inverse scattering transform [1, 2], also known as the nonlinear Fourier transform (NFT). A particularly important example for optical applications is the nonlinear Schrödinger equation (NLSE), which is one of the fundamental equations of nonlinear science, relevant to various fields of physics and practical engineering. However, NFT can also be used to analyze localized waveforms, rather than strictly to solve integrable equations. In particular, it allows one to describe a waveform or the evolution of coherent structures with fewer parameters than traditional harmonic Fourier analysis.
AB - The conventional (linear) Fourier transform is a widely used mathematical method in science and engineering. It allows the signal of interest to be represented as a set of spectral harmonics, which, in many situations, helps in understanding the structure and properties of that signal. In certain linear equations, where the spectral harmonics evolve independently, the Fourier transform provides a straightforward description of complex temporal or spatial dynamics. A related approach exists for certain classes of integrable nonlinear equations that can be solved via the inverse scattering transform [1, 2], also known as the nonlinear Fourier transform (NFT). A particularly important example for optical applications is the nonlinear Schrödinger equation (NLSE), which is one of the fundamental equations of nonlinear science, relevant to various fields of physics and practical engineering. However, NFT can also be used to analyze localized waveforms, rather than strictly to solve integrable equations. In particular, it allows one to describe a waveform or the evolution of coherent structures with fewer parameters than traditional harmonic Fourier analysis.
UR - https://www.mendeley.com/catalogue/75b2f327-1aad-3693-9973-49384b28a77d/
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105016257364&origin=inward
U2 - 10.1109/CLEO/EUROPE-EQEC65582.2025.11109113
DO - 10.1109/CLEO/EUROPE-EQEC65582.2025.11109113
M3 - Chapter
SN - 9798331512521
T3 - 2025 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2025
BT - 2025 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2025
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2025 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference
Y2 - 23 June 2025 through 27 June 2025
ER -
ID: 69782203