DYNAMICAL BEHAVIOR OF THE LONG WAVES IN THE NONLINEAR DISPERSIVE MEDIA THROUGH ANALYTICAL AND NUMERICAL INVESTIGATION

Enran Hou, Fuzhang Wang, Samir A. Salama and Mostafa M. A. Khater
Additional contact information
Enran Hou: College of mathematics, Huaibei Normal University, 235000 Huaibei, P. R. China
Fuzhang Wang: Nanchang Institute of Technology, Nanchang 330044, P. R. China
Samir A. Salama: Division of Biochemistry, Department of Pharmacology, College of Pharmacy, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
Mostafa M. A. Khater: Department of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, P. R. China5Department of Mathematics, Obour High Institute for Engineering and Technology, 11828 Cairo, Egypt

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-24

Abstract: This paper studies the well-known mathematical model’s analytical wave solutions (modified Benjamin–Bona–Mahony (BBM) equation), which demonstrates the propagation of long waves in the nonlinear dispersive media in a visual illusion. Six recent analytical and semi-analytical schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, sech–tanh expansion method, Adomian decomposition (ADD) method, El Kalla (EK) expansion method, variational iteration (VI) method) are applied to the considered model for constructing abundant analytical and semi-analytical novel solutions. This variety of solutions aims to investigate the analytical techniques’ accuracy by calculating the absolute error between analytical and semi-analytical solutions that shows the matching between them. The analytical results are sketched through two-dimensional (2D), three-dimensional (3D), contour plot, spherical plot and polar plot. The stability characterization of the analytical solutions is investigated through the Hamiltonian system’s features. The originality and novelty of this paper are discussed, along with previously published papers.

Keywords: Modified Benjamin–Bona–Mahony Equation; Analytical and Semi-Analytical Schemes and Solutions; Optical Illusion (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401314

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