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Nonlinear Fourier Transform as a Tool for Analyzing the Soliton Dynamics in Systems Obeying the Haus–Ginzburg–Landau Equation. / Chekhovskoy, I. S.; Shtyrina, O. V.; Fedoruk, M. P.
в: Bulletin of the Lebedev Physics Institute, Том 52, № Suppl 11, 6, 12.2025, стр. S1151-S1160.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Nonlinear Fourier Transform as a Tool for Analyzing the Soliton Dynamics in Systems Obeying the Haus–Ginzburg–Landau Equation
AU - Chekhovskoy, I. S.
AU - Shtyrina, O. V.
AU - Fedoruk, M. P.
N1 - Chekhovskoy, I. S. Nonlinear Fourier Transform as a Tool for Analyzing the Soliton Dynamics in Systems Obeying the Haus–Ginzburg–Landau Equation / I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk // Bulletin of the Lebedev Physics Institute. – 2025. – Vol. 52, No. S11. – P. S1151-S1160. – DOI 10.3103/S1068335625604571. – EDN UVQKGE. The work was supported by the Russian Science Foundation [grant no. 25-61-00010, https://rscf.ru/project/25-61-00010/ (M.P.F., problem statement; Ch.I.S., numerical studies). The research was supported by state assignement for fundamental research [FSUS-2025-0010 (Sh.O.V., theoretical studies].
PY - 2025/12
Y1 - 2025/12
N2 - We propose using the nonlinear Fourier transform (NFT) not as a method for integrating equations but as a tool for studying the properties of localized coherent structures in dissipative nonlinear systems. The effectiveness of using a discrete nonlinear spectrum for quantitatively describing the dynamics of optical pulses is demonstrated, even when the original model is not integrable. The application of this method is substantiated using the solution to the cubic Haus–Ginzburg–Landau equation (HGLE), which describes the generation of optical pulses from noise in passively mode-locked lasers. It is shown that stabilization of the discrete nonlinear spectrum serves as a reliable indicator of stable soliton generation. Additionally, algorithms for tracing individual discrete eigenvalues are proposed, including a machine-learning-based algorithm, which expands the toolbox for analyzing and automating the processing of data obtained using NFT.
AB - We propose using the nonlinear Fourier transform (NFT) not as a method for integrating equations but as a tool for studying the properties of localized coherent structures in dissipative nonlinear systems. The effectiveness of using a discrete nonlinear spectrum for quantitatively describing the dynamics of optical pulses is demonstrated, even when the original model is not integrable. The application of this method is substantiated using the solution to the cubic Haus–Ginzburg–Landau equation (HGLE), which describes the generation of optical pulses from noise in passively mode-locked lasers. It is shown that stabilization of the discrete nonlinear spectrum serves as a reliable indicator of stable soliton generation. Additionally, algorithms for tracing individual discrete eigenvalues are proposed, including a machine-learning-based algorithm, which expands the toolbox for analyzing and automating the processing of data obtained using NFT.
KW - Haus‒Ginzburg‒Landau equation
KW - discrete spectrum tracing
KW - inverse scattering method
KW - machine learning
KW - nonlinear Fourier transform
KW - нелинейное преобразование Фурье
KW - метод обратного рассеяния
KW - равнение Хауса–Гинзбурга–Ландау
KW - машинное обучение
KW - отслеживание дискретного спектра
UR - https://www.scopus.com/pages/publications/105031529576
UR - https://elibrary.ru/item.asp?id=89063135
UR - https://www.mendeley.com/catalogue/facf9a1b-d987-3417-8923-2ed6f04af4f8/
U2 - 10.3103/S1068335625604571
DO - 10.3103/S1068335625604571
M3 - Article
VL - 52
SP - S1151-S1160
JO - Bulletin of the Lebedev Physics Institute
JF - Bulletin of the Lebedev Physics Institute
SN - 1068-3356
IS - Suppl 11
M1 - 6
ER -
ID: 75599521