Abundant solitary and semi-analytical wave solutions of nonlinear shallow water wave regime model

Abstract

This article employs analytical and semi-analytical techniques for constructing accurate novel solitary wave solutions of the weakly nonlinear shallow-water wave regime (SWR) equation. The mathematical formula of the investigated model describes the dynamical behavior of the nonlinear shallow-water wave in a thin and dispersive medium. The extended tanh-expansion (ETE) method is applied for obtaining novel computational soliton wave solutions. Then, the Adomian decomposition (AD) scheme is used for checking the accuracy of the obtained computational solutions by comparing analytical and semi-analytical solutions. The obtained solutions are explained in some graphs in two-dimensional, three-dimensional, and contour plots. While, the matching between exact and approximate solutions is demonstrated through some various figures such as spline graphs in 2D, distribution graphs, scatter matrix graphs. All solutions are backed into the original model by Mathematica 12 for checking its validity.