Eur. Phys. J. Plus (2021) 136: 1024
https://doi.org/10.1140/epjp/s13360-021-01985-w

Regular Article

Superabundant novel solutions of the long waves mathematical modeling in shallow water with power-law nonlinearity in ocean beaches via three recent analytical schemes

¹ Department of Mathematics, Faculty of Science, Jiangsu University, 212013, Zhenjiang, China
² Department of Mathematics, Obour High Institute For Engineering and Technology, 11828, Cairo, Egypt
³ School of Management and Economics, Jiangsu University of Science and Technology, 212003, Zhenjiang, China

^a mostafa.khater2024@yahoo.com

Received: 21 May 2020
Accepted: 22 September 2021
Published online: 12 October 2021

Abstract

This research paper is connected with one of the most popular models in shallow water wave applications. The computational wave solutions of the Benjamin-Bona-Mahony-Peregrine (BBMP) equation with power-law nonlinearity are investigated via three new analytical schemes. This model is considered a natural extension of the well-known mathematical model called the Korteweg–de Vries (KdV) equation. The KdV has been used to study the shallow water wave behavior of long wavelengths and small amplitude. In contrast, the BBMP equation has been employed for the same purpose, but it concentrates on studying this kind of wave, especially in ocean beaches. Applying the modified auxiliary equation method (MAE) method, the direct algebraic (DA) method, and generalized Kudryashov (GK) method to the BBMP equation after harnessing suitable wave transformation gives plentiful unprecedented solitary wave solutions. Many novel solutions have been constructed through the suggested methods that have been built along with their 2D, 3D, and contour graphical configurations for clarity and exactitude.