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Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

Author

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  • Muhammad Shakeel

    (Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
    These authors contributed equally to this work.)

  • Attaullah

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

  • Essam Roshdy El-Zahar

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

  • Jae Dong Chung

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

Abstract

Using the new generalized exp-function method, we were able to derive significant novel closed form solutions to the nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of the new generalized exp-function method has been given. Many novel closed form solutions have been obtained in the form of hyperbolic, trigonometric, and rational function solutions. Using the computer application Wolfram Mathematica 10, we plotted 2D, 3D, and contour surfaces of closed form solutions found in this work. In the form of a table, the acquired results are compared to the known solutions in the existing literature.

Suggested Citation

  • Muhammad Shakeel & Attaullah & Essam Roshdy El-Zahar & Nehad Ali Shah & Jae Dong Chung, 2022. "Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1026-:d:777663
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Muhammad Shakeel & Qazi Mahmood Ul-Hassan & Jamshad Ahmad & Tauseef Naqvi, 2014. "Exact Solutions of the Time Fractional BBM-Burger Equation by Novel -Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-15, September.
    3. E. M. E. Zayed & Shorog Al-Joudi, 2010. "Applications of an Extended ( ð º â€² / ð º ) -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, August.
    Full references (including those not matched with items on IDEAS)

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