Nonlinear Fourier transform for analysis of coherent structures in dissipative systems

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

The conventional Fourier transform is widely used mathematical methods in science and technology. It allows representing the signal/field under study as a set of spectral harmonics, that it many situations simplify understanding of such signal/field. In some linear equations, where spectral harmonics evolve independently of each other, the Fourier transform provides a straightforward description of otherwise complex dynamics. Something similar is available for certain classes of nonlinear equations that are integrable using the inverse scattering transform [1, 2], also known as the nonlinear Fourier transform (NFT). Here we discuss potential of its application in dissipative, non-integrable systems to characterize coherent structures. We present a new approach for describing the evolution of a nonlinear system considering the cubic Ginzburg-Landau Equation (CGLE) as a particularly important example in the context of laser system modeling: (equation presented), (1) where δ > 0 is a distributed saturable absorber action and α > 0 describes the effect of distributed optical filtering. The CGLE has special solutions in the form of chirped dissipative solitons: U(z,t) = U01+iC(t) exp {iφz}, U0(t) = A/cosh (t/τ). The CGLE is not integrable, but we can still formally calculate the nonlinear spectrum of the optical field U(z,t) at each point z and study the evolution of the nonlinear spectrum by z. We anticipate that under certain conditions NFT might allow us to gain useful information concerning the evolution of coherent structures with fewer parameters compared to conventional Fourier harmonics analysis.

Язык оригиналаанглийский
Название основной публикацииEuropean Quantum Electronics Conference, EQEC_2019
ИздательOSA - The Optical Society
ISBN (электронное издание)9781557528209
СостояниеОпубликовано - 1 янв 2019
СобытиеEuropean Quantum Electronics Conference, EQEC_2019 - Munich, Великобритания
Продолжительность: 23 июн 201927 июн 2019

Серия публикаций

НазваниеOptics InfoBase Conference Papers
ТомPart F143-EQEC 2019

Конференция

КонференцияEuropean Quantum Electronics Conference, EQEC_2019
СтранаВеликобритания
ГородMunich
Период23.06.201927.06.2019

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    Chekhovskoy, I. S., Shtyrina, O. V., Fedoruk, M. P., Medvedev, S. B., & Turitsyn, S. K. (2019). Nonlinear Fourier transform for analysis of coherent structures in dissipative systems. В European Quantum Electronics Conference, EQEC_2019 [2019-ef_p_17] (Optics InfoBase Conference Papers; Том Part F143-EQEC 2019). OSA - The Optical Society.