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Chaotic Behaviour, Sensitivity Assessment, and New Analytical Investigation to Find Novel Optical Soliton Solutions of M-Fractional Kuralay-II Equation

Author

Listed:
  • J. R. M. Borhan

    (Department of Mathematics, Jashore University of Science and Technology, Jashore 7408, Bangladesh)

  • E. I. Hassan

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Arafa Dawood

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia)

  • Khaled Aldwoah

    (Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia)

  • Amani Idris A. Sayed

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

  • Ahmad Albaity

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

  • M. Mamun Miah

    (Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh
    Division of Mathematical and Physical Sciences, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan)

Abstract

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the ( G ′ G ′ + G + A ) -expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3 D ), contour, and two-dimensional (2 D ) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application.

Suggested Citation

  • J. R. M. Borhan & E. I. Hassan & Arafa Dawood & Khaled Aldwoah & Amani Idris A. Sayed & Ahmad Albaity & M. Mamun Miah, 2025. "Chaotic Behaviour, Sensitivity Assessment, and New Analytical Investigation to Find Novel Optical Soliton Solutions of M-Fractional Kuralay-II Equation," Mathematics, MDPI, vol. 13(13), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2207-:d:1695938
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    References listed on IDEAS

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    1. M. Mamun Miah & Faisal Alsharif & Md. Ashik Iqbal & J. R. M. Borhan & Mohammad Kanan, 2024. "Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization," Mathematics, MDPI, vol. 12(13), pages 1-22, June.
    2. Rafiq, Muhammad Hamza & Raza, Nauman & Jhangeer, Adil, 2023. "Dynamic study of bifurcation, chaotic behavior and multi-soliton profiles for the system of shallow water wave equations with their stability," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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