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

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.