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Dynamical Behavior of Solitary Waves for the Space-Fractional Stochastic Regularized Long Wave Equation via Two Distinct Approaches

Author

Listed:
  • Muneerah Al Nuwairan

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

  • Bashayr Almutairi

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

  • Anwar Aldhafeeri

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

Abstract

This study investigates the influence of multiplicative noise—modeled by a Wiener process—and spatial-fractional derivatives on the dynamics of the space-fractional stochastic Regularized Long Wave equation. By employing a complete discriminant polynomial system, we derive novel classes of fractional stochastic solutions that capture the complex interplay between stochasticity and nonlocality. Additionally, the variational principle, derived by He’s semi-inverse method, is utilized, yielding additional exact solutions that are bright solitons, bright-like solitons, kinky bright solitons, and periodic structures. Graphical analyses are presented to clarify how variations in the fractional order and noise intensity affect essential solution features, such as amplitude, width, and smoothness, offering deeper insight into the behavior of such nonlinear stochastic systems.

Suggested Citation

  • Muneerah Al Nuwairan & Bashayr Almutairi & Anwar Aldhafeeri, 2025. "Dynamical Behavior of Solitary Waves for the Space-Fractional Stochastic Regularized Long Wave Equation via Two Distinct Approaches," Mathematics, MDPI, vol. 13(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2193-:d:1695153
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    References listed on IDEAS

    as
    1. Nisrine Maarouf & Hicham Maadan & Khalid Hilal, 2021. "Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-11, February.
    2. Ji-Huan He & Wei-Fan Hou & Chun-Hui He & Tareq Saeed & Tasawar Hayat, 2021. "Variational Approach To Fractal Solitary Waves," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-5, November.
    3. Wael W. Mohammed & Mohammed Alshammari & Clemente Cesarano & Sultan Albadrani & M. El-Morshedy, 2022. "Brownian Motion Effects on the Stabilization of Stochastic Solutions to Fractional Diffusion Equations with Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-9, April.
    4. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
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