Characterization of coherent structures in dissipative systems using nonlinear Fourier transform

I. S. Chekhovskoy; O. V. Shtyrina; M. P. Fedoruk; S. B. Medvedev; S. K. Turitsyn

doi:10.1117/12.2555076

Characterization of coherent structures in dissipative systems using nonlinear Fourier transform

I. S. Chekhovskoy^*, O. V. Shtyrina, M. P. Fedoruk, S. B. Medvedev, S. K. Turitsyn

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

Abstract

We demonstrated how the nonlinear Fourier transform based on the Zakharov-Shabat spectral problem can be used to characterise coherent structures in dissipative systems. We consider as a particular, albeit important practical example model equation that is widely used to analyse laser radiation and demonstrate that dissipative solitons can be described by a limited number of degrees of freedom - discrete eigenvalues. Our approach can be applied for signal processing in a number of optical systems, from lasers to micro-resonators.

Original language	English
Article number	113581B
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	11358
DOIs	https://doi.org/10.1117/12.2555076
Publication status	Published - 1 Apr 2020
Event	Nonlinear Optics and its Applications 2020 - Virtual, Online, France Duration: 6 Apr 2020 → 10 Apr 2020

Bibliographical note

Copyright 2020 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Keywords

Cubic Ginzburg-Landau equation
Dissipative systems
Nonlinear Fourier transform
Nonlinear Schrödinger equation
Numerical simulations

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10.1117/12.2555076

Characterization of coherent structures
Copyright 2020 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
Final published version, 6.1 MB

Cite this

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title = "Characterization of coherent structures in dissipative systems using nonlinear Fourier transform",

abstract = "We demonstrated how the nonlinear Fourier transform based on the Zakharov-Shabat spectral problem can be used to characterise coherent structures in dissipative systems. We consider as a particular, albeit important practical example model equation that is widely used to analyse laser radiation and demonstrate that dissipative solitons can be described by a limited number of degrees of freedom - discrete eigenvalues. Our approach can be applied for signal processing in a number of optical systems, from lasers to micro-resonators.",

keywords = "Cubic Ginzburg-Landau equation, Dissipative systems, Nonlinear Fourier transform, Nonlinear Schr{\"o}dinger equation, Numerical simulations",

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note = "Copyright 2020 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. ; Nonlinear Optics and its Applications 2020 ; Conference date: 06-04-2020 Through 10-04-2020",

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AU - Chekhovskoy, I. S.

AU - Shtyrina, O. V.

AU - Fedoruk, M. P.

AU - Medvedev, S. B.

AU - Turitsyn, S. K.

N1 - Copyright 2020 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We demonstrated how the nonlinear Fourier transform based on the Zakharov-Shabat spectral problem can be used to characterise coherent structures in dissipative systems. We consider as a particular, albeit important practical example model equation that is widely used to analyse laser radiation and demonstrate that dissipative solitons can be described by a limited number of degrees of freedom - discrete eigenvalues. Our approach can be applied for signal processing in a number of optical systems, from lasers to micro-resonators.

AB - We demonstrated how the nonlinear Fourier transform based on the Zakharov-Shabat spectral problem can be used to characterise coherent structures in dissipative systems. We consider as a particular, albeit important practical example model equation that is widely used to analyse laser radiation and demonstrate that dissipative solitons can be described by a limited number of degrees of freedom - discrete eigenvalues. Our approach can be applied for signal processing in a number of optical systems, from lasers to micro-resonators.

KW - Cubic Ginzburg-Landau equation

KW - Dissipative systems

KW - Nonlinear Fourier transform

KW - Nonlinear Schrödinger equation

KW - Numerical simulations

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DO - 10.1117/12.2555076

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VL - 11358

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

M1 - 113581B

T2 - Nonlinear Optics and its Applications 2020

Y2 - 6 April 2020 through 10 April 2020

ER -

Characterization of coherent structures in dissipative systems using nonlinear Fourier transform

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