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

Abdel-Haleem Abdel-Aty, Mostafa M. A. Khater, Raghda A. M. Attia and Hichem Eleuch
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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
Mostafa M. A. Khater: Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, China
Raghda A. M. Attia: Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, China

Mathematics, 2020, vol. 8, issue 5, 1-11

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.

Keywords: the modified Riccati expansion method; Adomian decomposition method (ADM); weakly nonlinear shallow-water wave regime; analytical and semi-analytical wave solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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