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Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells

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  • Abdel-Haleem Abdel-Aty

    (Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia
    Physics Department, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt)

  • Mostafa M. A. Khater

    (Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, China
    Department of Mathematics, El Obour Institutes, 11828 Cairo, Egypt)

  • Raghda A. M. Attia

    (Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, China
    Department of Basic Science, Higher Technological Institute, 44634 10th of Ramadan City, Egypt)

  • Hichem Eleuch

    (Department of Applied Science and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi 59911, UAE
    Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA)

Abstract

In this paper, the weakly nonlinear shallow-water wave model is mathematically investigated by applying the modified Riccati-expansion method and Adomian decomposition method. This model is used to describe the propagation of waves in weakly nonlinear and dispersive media. We obtain exact and solitary wave solutions of this model by using the modified Riccati-expansion method then using these solutions to determine the boundary and initial conditions. These conditions are employed to evaluate the semi-analytical wave solutions and calculate the absolute value of error. The values of absolute error show the accuracy of the obtained solutions. Some solutions are sketched to show the perspective view of the solution of this model. Moreover, the novelty of the obtained solutions is illustrated by showing the similarity and differences between our and previous solutions of the model.

Suggested Citation

  • Abdel-Haleem Abdel-Aty & Mostafa M. A. Khater & Raghda A. M. Attia & Hichem Eleuch, 2020. "Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:697-:d:353231
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    References listed on IDEAS

    as
    1. Jin-Fu Liang & Xun Wang, 2019. "Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, July.
    2. Lamine Thiam & Xi-zhong Liu, 2019. "Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation," Complexity, Hindawi, vol. 2019, pages 1-9, November.
    3. Ralph Brinks & Annika Hoyer, 2018. "Illness-death model: statistical perspective and differential equations," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 743-754, October.
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