### Abstract

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 |

### Fingerprint

### Cite this

*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

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*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, 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) , Munich, Germany, 23/06/19. https://doi.org/10.1109/CLEOE-EQEC.2019.8872485

**Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems.** / Chekhovskoy, I.S.; Shtyrina, Olga V.; Fedoruk, Mikhail P.; Medvedev, Sergey B.; Turitsyn, Sergei K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems

AU - Chekhovskoy, I.S.

AU - Shtyrina, Olga V.

AU - Fedoruk, Mikhail P.

AU - Medvedev, Sergey B.

AU - Turitsyn, Sergei K.

PY - 2019/10/17

Y1 - 2019/10/17

N2 - 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: $i{\partial U \over \partial z} + {1 \over 2} {\partial^{2} U \over \partial t^{2}} + \vert U \vert^{2} U -i \left(\sigma U + \alpha {\partial^{2}U \over \partial t^{2}} + \delta \vert U \vert^{2} U \right) = 0,$.

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

UR - https://ieeexplore.ieee.org/document/8872485?dld=YXN0b24uYWMudWs%3D&source=SEARCHALERT

UR - http://www.scopus.com/inward/record.url?scp=85074669011&partnerID=8YFLogxK

U2 - 10.1109/CLEOE-EQEC.2019.8872485

DO - 10.1109/CLEOE-EQEC.2019.8872485

M3 - Conference contribution

SN - 978-1-7281-0470-6

T3 - 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019

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

PB - IEEE

ER -