Prorogation of waves in shallow water through unidirectional Dullin–Gottwald–Holm model; computational simulations

Abstract

This paper investigates novel solitary wave solutions of the unidirectional Dullin–Gottwald–Holm model and employs the modified Khater (MKhat) method for studying the dynamical characterization of the prorogation of waves in shallow water. There are various solution types obtained such as kink, periodic, cone, anti-kink, etc. The accuracy of these solutions is checked by implementing He’s variational iteration technique. The analytical and numerical solutions are numerically simulated through 3D, 2D and contour plots for a visual explanation of the shallow water waves’ propagation and the match between both kinds of solutions. Additionally, the interaction between solutions is explained by some stream plots to show the local direction of the vector field at each point and a roughly uniform density throughout the property, which indicates no background scalar field. The novelty of the study’s solutions is explained by comparing it with the previously published articles.