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Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences

Author

Listed:
  • Khudhayr A. Rashedi

    (Deparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Musawa Yahya Almusawa

    (Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia)

  • Hassan Almusawa

    (Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia)

  • Tariq S. Alshammari

    (Deparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Adel Almarashi

    (Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia)

Abstract

The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and conformable fractional derivatives. The obtained solutions are expressed in trigonometric, hyperbolic, and rational forms, highlighting the adaptability and efficacy of the proposed approach. To enhance the understanding of the results, the solutions are visualized using 2D representations for fractional-order variations and 3D plots for integer-type solutions, supported by detailed contour plots. The findings contribute to a deeper understanding of nonlinear wave–wave interactions and the underlying dynamics governed by fractional-order derivatives. This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling.

Suggested Citation

  • Khudhayr A. Rashedi & Musawa Yahya Almusawa & Hassan Almusawa & Tariq S. Alshammari & Adel Almarashi, 2024. "Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences," Mathematics, MDPI, vol. 13(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:84-:d:1555714
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    References listed on IDEAS

    as
    1. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    2. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
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