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Study of Optical Solitons and Quasi-Periodic Behaviour for the Fractional Cubic Quintic Nonlinear Pulse Propagation Model

Author

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  • Lotfi Jlali

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia)

  • Syed T. R. Rizvi

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54840, Pakistan)

  • Sana Shabbir

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54840, Pakistan)

  • Aly R. Seadawy

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

Abstract

This study explores analytical soliton solutions for the cubic–quintic time-fractional nonlinear non-paraxial pulse transmission model. This versatile model finds numerous uses in fiber optic communication, nonlinear optics, and optical signal processing. The strength of the quintic and cubic nonlinear components plays a crucial role in nonlinear processes, such as self-phase modulation, self-focusing, and wave combining. The fractional nonlinear Schrödinger equation (FNLSE) facilitates precise control over the dynamic properties of optical solitons. Exact and methodical solutions include those involving trigonometric functions, Jacobian elliptical functions (JEFs), and the transformation of JEFs into solitary wave (SW) solutions. This study reveals that various soliton solutions, such as periodic, rational, kink, and SW solitons, are identified using the complete discrimination polynomial methods (CDSPM). The concepts of chaos and bifurcation serve as the framework for investigating the system qualitatively. We explore various techniques for detecting chaos, including three-dimensional and two-dimensional graphs, time-series analysis, and Poincarè maps. A sensitivity analysis is performed utilizing a variety of initial conditions.

Suggested Citation

  • Lotfi Jlali & Syed T. R. Rizvi & Sana Shabbir & Aly R. Seadawy, 2025. "Study of Optical Solitons and Quasi-Periodic Behaviour for the Fractional Cubic Quintic Nonlinear Pulse Propagation Model," Mathematics, MDPI, vol. 13(13), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2117-:d:1689761
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    2. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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