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Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method

Author

Listed:
  • Muhammad Shakeel

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

  • Attaullah

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

  • Mohammed Kbiri Alaoui

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

  • Ahmed M. Zidan

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

  • Nehad Ali Shah

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

  • Wajaree Weera

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary wave solutions of one-dimensional nonlinear LWE. Using the computer program Wolfram Mathematica 10, these new exact and solitary wave solutions of the LWE are derived as trigonometric function, periodic solitary wave, rational function, hyperbolic function, bright and dark solitons solutions, sinh, cosh, and sech 2 function solutions of the LWE. These solutions represent the electrostatic potential and pressure for LWE as well as the graphical representation of electrostatic potential and pressure.

Suggested Citation

  • Muhammad Shakeel & Attaullah & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Wajaree Weera, 2022. "Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3400-:d:918836
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    References listed on IDEAS

    as
    1. 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.
    2. Helal, M.A. & Seadawy, A.R. & Zekry, M.H., 2014. "Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1094-1103.
    3. Seadawy, Aly R., 2015. "Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 124-131.
    4. Attia Rani & Muhammad Shakeel & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Prem Junsawang, 2022. "Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    Full references (including those not matched with items on IDEAS)

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