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Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative

Author

Listed:
  • Anwar Aldhafeeri

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Muneerah Al Nuwairan

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

Abstract

In this paper, we investigate the time M-fractional modified nonlinear Schrödinger equation that describes the propagation of rogue waves in deep water. Periodic, solitary, and kink (or anti-kink) wave solutions are discussed using the bifurcation theory for planar integrable systems. Some new wave solutions are constructed using the first integral for the traveling wave system. The degeneracy of the obtained solutions is investigated by using the transition between orbits. We visually explore some of the solutions using graphical representations for different values of the fractional order.

Suggested Citation

  • Anwar Aldhafeeri & Muneerah Al Nuwairan, 2023. "Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative," Mathematics, MDPI, vol. 11(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1219-:d:1085644
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    References listed on IDEAS

    as
    1. Wafaa B. Rabie & Hamdy M. Ahmed & Walid Hamdy, 2023. "Exploration of New Optical Solitons in Magneto-Optical Waveguide with Coupled System of Nonlinear Biswas–Milovic Equation via Kudryashov’s Law Using Extended F-Expansion Method," Mathematics, MDPI, vol. 11(2), pages 1-28, January.
    2. Mohammed Alabedalhadi & Mohammed Shqair & Shrideh Al-Omari & Mohammed Al-Smadi, 2023. "Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    3. M. E. Elbrolosy & A. A. Elmandouh & Abdellatif Ben Makhlouf, 2022. "Dynamical Behaviour of Conformable Time-Fractional Coupled Konno-Oono Equation in Magnetic Field," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, June.
    Full references (including those not matched with items on IDEAS)

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