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Open AccessArticle

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

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Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia
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Physics Department, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt
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Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, China
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Department of Mathematics, El Obour Institutes, 11828 Cairo, Egypt
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Department of Basic Science, Higher Technological Institute, 44634 10th of Ramadan City, Egypt
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Department of Applied Science and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi 59911, UAE
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Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 697; https://doi.org/10.3390/math8050697
Received: 24 March 2020 / Revised: 18 April 2020 / Accepted: 20 April 2020 / Published: 2 May 2020
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
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. View Full-Text
Keywords: the modified Riccati expansion method; Adomian decomposition method (ADM); weakly nonlinear shallow-water wave regime; analytical and semi-analytical wave solutions the modified Riccati expansion method; Adomian decomposition method (ADM); weakly nonlinear shallow-water wave regime; analytical and semi-analytical wave solutions
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MDPI and ACS Style

Abdel-Aty, A.-H.; Khater, M.M.A.; Attia, R.A.M.; Eleuch, H. Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells. Mathematics 2020, 8, 697. https://doi.org/10.3390/math8050697

AMA Style

Abdel-Aty A-H, Khater MMA, Attia RAM, Eleuch H. Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells. Mathematics. 2020; 8(5):697. https://doi.org/10.3390/math8050697

Chicago/Turabian Style

Abdel-Aty, Abdel-Haleem; Khater, Mostafa M.A.; Attia, Raghda A.M.; Eleuch, Hichem. 2020. "Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells" Mathematics 8, no. 5: 697. https://doi.org/10.3390/math8050697

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