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Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules

Author

Listed:
  • Attaullah

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

  • Muhammad Shakeel

    (Department of Mathematics, University of Wah, Wah Cantonment, Punjab 47040, Pakistan)

  • 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

A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions to Nonlinear Evolution Equation (NLEE) containing parameters of particular importance in biophysics and nanobiosciences. For this equation, we find trigonometric, hyperbolic, rational, and exponential function solutions, as well as soliton-like pulse solutions. A comparison with other approach indicates the legitimacy of the approach we devised as well as the fact that our method offers extra solutions. Finally, we plot 2D, 3D and contour visualizations of the exact results that we observed using our approach using appropriate parameter values with the help of software Mathematica 10.

Suggested Citation

  • Attaullah & Muhammad Shakeel & Nehad Ali Shah & Jae Dong Chung, 2022. "Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:851-:d:766396
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    References listed on IDEAS

    as
    1. 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.
    2. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
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    Cited by:

    1. 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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