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Nonlinear Dynamical Analysis and New Solutions of the Space-Fractional Stochastic Davey–Stewartson Equations for Nonlinear Water Waves

Author

Listed:
  • Adel Elmandouh

    (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)

  • M. M. El-Dessoky

    (Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

We investigate how novelly generated solutions of the stochastic space-fractional Davey–Stewartson equations are affected by spatial-fractional derivatives and multiplicative Brownian motion (in the Stratonovich sense). These equations model the behavior of weakly nonlinear water waves on a fluid surface. By applying the qualitative theory of planar systems, some new fractional and stochastic solutions are obtained. These solutions gain significance from the application of Davey–Stewartson equations to the theory of turbulence for plasma waves, as they can explain several fascinating physical phenomena. Some solutions are graphically displayed to illustrate the influence of noise strength and fractional derivatives on the obtained solutions. These effects influence the solution’s amplitude and width, as well as its smoothness.

Suggested Citation

  • Adel Elmandouh & Muneerah Al Nuwairan & M. M. El-Dessoky, 2025. "Nonlinear Dynamical Analysis and New Solutions of the Space-Fractional Stochastic Davey–Stewartson Equations for Nonlinear Water Waves," Mathematics, MDPI, vol. 13(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:692-:d:1596170
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    References listed on IDEAS

    as
    1. Wael W. Mohammed & Naveed Iqbal & Thongchai Botmart, 2022. "Additive Noise Effects on the Stabilization of Fractional-Space Diffusion Equation Solutions," Mathematics, MDPI, vol. 10(1), pages 1-14, January.
    2. Qi, Jianming & Cui, Qinghua & Bai, Leiqiang & Sun, Yiqun, 2024. "Investigating exact solutions, sensitivity, and chaotic behavior of multi-fractional order stochastic Davey–Sewartson equations for hydrodynamics research applications," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    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.
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