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The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Author

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  • Farah M. Al-Askar
  • Wael W. Mohammed
  • Qura tul Ain

Abstract

This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

Suggested Citation

  • Farah M. Al-Askar & Wael W. Mohammed & Qura tul Ain, 2022. "The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, August.
    • Handle: RePEc:hin:jnlamp:1534067
    DOI: 10.1155/2022/1534067
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    Cited by:

    1. Tahira Sumbal Shaikh & Muhammad Zafarullah Baber & Nauman Ahmed & Naveed Shahid & Ali Akgül & Manuel De la Sen, 2023. "On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    2. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    3. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    4. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Elkhateeb S. Aly, 2023. "The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative," Mathematics, MDPI, vol. 11(6), pages 1-11, March.

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