Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model

Abstract

In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view of group theory, the proposed analytical methods in our article are based on symmetry, and effectively solve those problems which actually possess explicit or implicit symmetry. This model is a vital model in shallow water phenomena where it demonstrates the wave surface propagating in both directions. The obtained analytical solutions are explained by plotting them through 3D, 2D, and contour sketches. These solutions’ accuracy is also tested by calculating the absolute error between them and evaluated numerical results by the Adomian decomposition (AD) method and variational iteration (VI) method. The considered numerical schemes were applied based on constructed initial and boundary conditions through the obtained analytical solutions via the MDA, and MK methods which show the synchronization between computational and numerical obtained solutions. This coincidence between the obtained solutions is explained through two-dimensional and distribution plots. The applied methods’ symmetry is shown through comparing their obtained results and showing the matching between both obtained solutions (analytical and numerical).