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On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations

Author

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  • Wael W. Mohammed

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Farah M. Al-Askar

    (Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

Abstract

In this paper, we take into account the coupled stochastic Korteweg–De Vries (CSKdV) equations in the Itô sense. Using the mapping method, new trigonometric, rational, hyperbolic, and elliptic stochastic solutions are obtained. These obtained solutions can be applied to the analysis of a wide variety of crucial physical phenomena because the coupled KdV equations have important applications in various fields of physics and engineering. Also, it is used in the design of optical fiber communication systems, which transmit information using soliton-like waves. The dynamic performance of the various obtained solutions are depicted using 3D and 2D curves in order to interpret the effects of multiplicative noise. We conclude that multiplicative noise influences the behavior of the solutions of CSKdV equations and stabilizes them.

Suggested Citation

  • Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2023. "On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3506-:d:1216850
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    References listed on IDEAS

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    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2022. "The Analytical Solutions of the Stochastic mKdV Equation via the Mapping Method," Mathematics, MDPI, vol. 10(22), pages 1-9, November.
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    Cited by:

    1. Hail S. Alrashdi & Osama Moaaz & Khaled Alqawasmi & Mohammad Kanan & Mohammed Zakarya & Elmetwally M. Elabbasy, 2024. "Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case," Mathematics, MDPI, vol. 12(8), pages 1-15, April.

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