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Propagation of chirped periodic and localized waves with higher-order effects through optical fibers

Author

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  • Daoui, Abdel Kader
  • Messouber, Abdelouahab
  • Triki, Houria
  • Zhou, Qin
  • Biswas, Anjan
  • Liu, Wenjun
  • Alzahrani, Abdullah K.
  • Belic, Milivoj R.

Abstract

We study the propagation properties of nonlinear periodic waves in an optical fiber medium exhibiting Kerr dispersion and quintic nonlinearity. The quintic derivative nonlinear Schrödinger equation is applied to model the evolution of femtosecond light waves in such system. Unlike periodic structures in Kerr media, the novel waves possess a nonlinear chirp which varies with their intensity. In addition to the linear part, the pulse chirp also includes two intensity dependent chirping terms. The conditions on fiber parameters for the existence of the newly found periodic waves are presented. A wide variety of solitary pulse shapes including the bright, dark, kink, anti-kink, and gray solitary waves are obtained in the long-wave limit. Our results show that Kerr dispersion plays a crucial role in introducing a nonlinear chirp for the periodic and solitary waves. Finally, the stability of these nonlinearly chirped solutions is numerically studied under the finite perturbations.

Suggested Citation

  • Daoui, Abdel Kader & Messouber, Abdelouahab & Triki, Houria & Zhou, Qin & Biswas, Anjan & Liu, Wenjun & Alzahrani, Abdullah K. & Belic, Milivoj R., 2021. "Propagation of chirped periodic and localized waves with higher-order effects through optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002265
    DOI: 10.1016/j.chaos.2021.110873
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    References listed on IDEAS

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    1. Yan, Zhenya & Chow, K.W. & Malomed, Boris A., 2009. "Exact stationary wave patterns in three coupled nonlinear Schrödinger/Gross–Pitaevskii equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3013-3019.
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    Cited by:

    1. Yang, Sheng-Xiong & Wang, Yu-Feng & Zhang, Xi, 2023. "Conservation laws, Darboux transformation and localized waves for the N-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Zhou, Qin & Triki, Houria & Xu, Jiakun & Zeng, Zhongliang & Liu, Wenjun & Biswas, Anjan, 2022. "Perturbation of chirped localized waves in a dual-power law nonlinear medium," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Rizvi, Syed T.R. & Seadawy, Aly R. & Raza, Umar, 2022. "Some advanced chirped pulses for generalized mixed nonlinear Schrödinger dynamical equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Seadawy, Aly R. & Rizvi, Syed T.R. & Sohail, Muhammad & Ali, Kashif, 2022. "Nonlinear model under anomalous dispersion regime: Chirped periodic and solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Iskenderoglu, Gulistan & Kaya, Dogan, 2022. "Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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