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Quasi-analytical Perturbation Analysis of the Generalized Nonlinear Schrödinger Equation

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Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

The Generalized Nonlinear Schrödinger Equation (GNLSE) finds several applications, especially in describing pulse propagation in nonlinear fiber optics. A well-known and thoroughly studied phenomenon in nonlinear wave propagation is that of modulation instability (MI). MI is approached as a weak perturbation to a pump and the analysis is based on preserving those terms linear on the perturbation and disregarding higher-order terms. In this sense, the linear MI analysis is relevant to the understanding of the onset of many other nonlinear phenomena, but its application is limited to the evolution of the perturbation over short distances. In this work, we propose quasi-analytical approximations to the propagation of a perturbation consisting of additive white noise that go beyond the linear modulation instability analysis. Moreover, we show these approximations to be in excellent agreement with numerical simulations and experimental measurements.

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Acknowledgments

We gratefully acknowledge S. Radic for hosting J. B.’s research stay at the Photonic Systems Group, UCSD, financial support from project PIP 2015, CONICET, Argentina, and from ONR Global through the Visiting Scientists Program.

Author information

Authors and Affiliations

  1. Instituto Balseiro (IB), Río Negro, Argentina

    J. Bonetti, S. M. Hernandez & D. F. Grosz

  2. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina

    J. Bonetti & P. I. Fierens

  3. Instituto Tecnológico de Buenos Aires (ITBA), Buenos Aires, Argentina

    P. I. Fierens & D. F. Grosz

  4. Department of Electrical and Computer Engineering, University of California San Diego, San Diego, CA, USA

    E. Temprana

Authors
  1. J. Bonetti
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  2. S. M. Hernandez
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  3. P. I. Fierens
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  4. E. Temprana
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  5. D. F. Grosz
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Corresponding author

Correspondence to P. I. Fierens .

Editor information

Editors and Affiliations

  1. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Visarath In

  2. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Patrick Longhini

  3. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Antonio Palacios

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Bonetti, J., Hernandez, S.M., Fierens, P.I., Temprana, E., Grosz, D.F. (2019). Quasi-analytical Perturbation Analysis of the Generalized Nonlinear Schrödinger Equation. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-10892-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-10892-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10891-5

  • Online ISBN: 978-3-030-10892-2

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