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Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves

Author

Listed:
  • Attia Rani

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

  • Muhammad Shakeel

    (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.)

  • Prem Junsawang

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

Abstract

Heimburg and Jackson devised a mathematical model known as the Heimburg model to describe the transmission of electromechanical pulses in nerves, which is a significant step forward. The major objective of this paper was to examine the dynamics of the Heimburg model by extracting closed-form wave solutions. The proposed model was not studied by using analytical techniques. For the first time, innovative analytical solutions were investigated using the exp − φ ξ -expansion method to illustrate the dynamic behavior of the electromechanical pulse in a nerve. This approach generates a wide range of general and broad-spectral solutions with unknown parameters. For the definitive value of these constraints, the well-known periodic- and kink-shaped solitons were recovered. By giving different values to the parameters, the 3D, 2D, and contour forms that constantly modulate in the form of an electromechanical pulse traveling through the axon in the nerve were created. The discovered solutions are innovative, distinct, and useful and might be crucial in medicine and biosciences.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3372-:d:916885
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    References listed on IDEAS

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    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. Ren, Yu-Jie & Zhang, Hong-Qing, 2006. "A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 959-979.
    3. El-Wakil, S.A. & Abdou, M.A., 2007. "New exact travelling wave solutions using modified extended tanh-function method," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 840-852.
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    Cited by:

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