@inproceedings{cd30a2257e824dee85d367e6dcf9d8c2,

title = "Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems",

abstract = "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: $i{\partial U \over \partial z} + {1 \over 2} {\partial^{2} U \over \partial t^{2}} + \vert U \vert^{2} U -i \left(\sigma U + \alpha {\partial^{2}U \over \partial t^{2}} + \delta \vert U \vert^{2} U \right) = 0,$.",

author = "I.S. Chekhovskoy and Shtyrina, {Olga V.} and Fedoruk, {Mikhail P.} and Medvedev, {Sergey B.} and Turitsyn, {Sergei K.}",

year = "2019",

month = oct,

day = "17",

doi = "10.1109/CLEOE-EQEC.2019.8872485",

language = "English",

isbn = "978-1-7281-0470-6",

series = "2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019",

publisher = "IEEE",

booktitle = "2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019",

address = "United States",

note = "2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) ; Conference date: 23-06-2019 Through 27-06-2019",

}