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Pyragas method and chaos in higher-order nonlinear Schrödinger equation in an optical fiber

  • Regular Article - Optical Phenomena and Photonics
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Abstract

Various dynamic behaviors of the higher-order nonlinear Schrödinger (HNLS) equation are investigated in an optical fiber. The governing model is converted into the planar dynamical system with the help of Galilean transformation. Through the effective potential and their corresponding phase portrait, the effects of the self-phase modulation and the quintic nonlinearity on the unperturbed system are addressed. Moreover, we performed different numerical tools such as time series, phase portraits as well as the Poincaré section, which show that the perturbed system transits from the quasi-periodic state to the chaotic state according to the frequency \(\omega \) and the strength of the external perturbation \(f_{0}\). The chaotic phenomena can be controlled by using the Pyragas method. This work finds its applications in broadband telecommunications which extend in the infrared spectral region, the doping of optical fiber as well as the encryption of information.

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Data Availability

This manuscript has no associated data or the data will not be deposited. [Data sharing not applicable to this article as no data sets were generated or analyzed during the current study.]

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Author information

Authors and Affiliations

  1. Higher Teachers’ Training College, University of Maroua, P.O. Box 55, Maroua, Cameroon

    M. Bahar, B. B. Mouhammadoul &  Alim

  2. Faculty of Sciences, University of Maroua, P.O. Box 814, Maroua, Cameroon

    C. G. L. Tiofack

  3. National Advanced School of Engineering, University of Maroua, P.O. Box 46, Maroua, Cameroon

    A. Mohamadou

  4. The Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada costiera 11, I-34014, Trieste, Italy

    A. Mohamadou

Authors
  1. M. Bahar
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  2. B. B. Mouhammadoul
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  3. C. G. L. Tiofack
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  4. Alim
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  5. A. Mohamadou
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Contributions

CGLT conceived the idea of the present work. MB and AA performed the analytical and numerical computations. AM refined the analytical calculations. BBM, MB and AA conducted the interpretation of the results. MB wrote an initial draft. AM finalized the article.

Corresponding author

Correspondence to B. B. Mouhammadoul.

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Bahar, M., Mouhammadoul, B.B., Tiofack, C.G.L. et al. Pyragas method and chaos in higher-order nonlinear Schrödinger equation in an optical fiber. Eur. Phys. J. D 76, 104 (2022). https://doi.org/10.1140/epjd/s10053-022-00435-1

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