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Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method

Author

Listed:
  • Shumaila Naz

    (Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan
    These authors contributed equally to this work and are co-first authors.)

  • Attia Rani

    (Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan)

  • Muhammad Shakeel

    (Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
    These authors contributed equally to this work and are co-first authors.)

  • Jae Dong Chung

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea)

Abstract

The Riemann wave equation is an intriguing nonlinear equation in the areas of tsunamis and tidal waves in oceans, electromagnetic waves in transmission lines, magnetic and ionic sound radiations in plasmas, static and uniform media, etc. In this innovative research, the analytical solutions of the fractional Riemann wave equation with a conformable derivative were retrieved as a special case, and broad-spectrum solutions with unknown parameters were established with the improved (G’/G)-expansion method. For the various values of these unknown parameters, the renowned periodic, singular, and anti-singular kink-shaped solitons were retrieved. Using the Maple software, we investigated the solutions by drawing the 3D, 2D, and contour plots created to analyze the dynamic behavior of the waves. The discovered solutions might be crucial in the disciplines of science and ocean engineering.

Suggested Citation

  • Shumaila Naz & Attia Rani & Muhammad Shakeel & Nehad Ali Shah & Jae Dong Chung, 2022. "Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method," Mathematics, MDPI, vol. 10(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4171-:d:966255
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    References listed on IDEAS

    as
    1. Ahmed Kajouni & Ahmed Chafiki & Khalid Hilal & Mohamed Oukessou, 2021. "A New Conformable Fractional Derivative and Applications," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-5, November.
    2. Wenfeng He & Nana Chen & Ioannis Dassios & Nehad Ali Shah & Jae Dong Chung, 2021. "Fractional System of Korteweg-De Vries Equations via Elzaki Transform," Mathematics, MDPI, vol. 9(6), pages 1-18, March.
    Full references (including those not matched with items on IDEAS)

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