Unidirectional shallow water wave model; Computational simulations

Abstract

This article delves into new solitary wave solutions for the unidirectional Dullin–Gottwald–Holm (DGH) model. Dynamical characterizations of wave prorogation in shallow water are investigated using two modern analytical approaches (generalized Tanh-function (GTF) methods and the improved Fan-expansion (IFE) method). In addition, the solutions achieved by using He’s variational iteration (He’s VI) approach are examined by demonstrating agreement between the built analytical and numerical solutions, providing more evidence for the correctness of the acquired results. Numerous sorts of solutions are produced, including solitary, shock, kink, periodic, cone, anti-kink, etc. The numerical simulations of these solutions are shown as 3D, 2D, and contour graphs. Some stream graphs illustrate the local direction of the vector field at each point, and a relatively uniform density across the property, indicating no background scalar field, further elucidates the interaction between solutions. In light of prior literature, the authors of this research provide an explanation for the originality of their findings. The comparison reveals up-to-date analytical and numerical solutions to the model under study.