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

Original language | English |
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Title of host publication | 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019 |

Publisher | IEEE |

ISBN (Electronic) | 978-1-7281-0469-0 |

ISBN (Print) | 978-1-7281-0470-6 |

DOIs | |

Publication status | Published - 17 Oct 2019 |

Event | 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany Duration: 23 Jun 2019 → 27 Jun 2019 |

### Publication series

Name | 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019 |
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### Conference

Conference | 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) |
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Country | Germany |

City | Munich |

Period | 23/06/19 → 27/06/19 |

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## Cite this

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. In

*2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019*[8872485] (2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019). IEEE. https://doi.org/10.1109/CLEOE-EQEC.2019.8872485