(9)Dispersive soliton solutions for shallow water wave system and modified Benjamin-Bona-Mahony equations via applications of mathematical methods
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Asghar Alia, Aly R. Seadawyb,∗
a Mathematics Department, University of Education, Lahore, Pakistan
b Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
Received 1 June 2020; received in revised form 19 June 2020; accepted 19 June 2020
Available online 23 July 2020
Abstract
We have utilized three novel methods, called generalized direct algebraic, modified F-expansion and improved simple equation methods
to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation. After
substituting particular values of the parameters, different solitary wave solutions are derived from the exact traveling wave solutions. It is
shown that these employed methods are more powerful tools for nonlinear wave equations.
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Keywords: System of shallow water wave equations; Modified Benjamin-Bona-Mahony equation; Generalized direct algebraic method; Improved simple
equation method; Modified F-expansion method; Traveling wave solutions; Solitary wave solutions.