Plenty of analytical and semi-analytical wave solutions of shallow water beneath gravity

This article studies novel soliton wave solutions of the nonlinear fractional ill-posed Boussinesq (NLFIPB) dynamic wave equation by applying the extended Riccati-expansion (ERE) method. Jacques Hadamard has formulated the investigated model to figure out the dynamic characterizations of waves in shallow water under gravity. The obtained solutions are explained through some sketches in 2D and 3D and contour plots. At the same time, the results' accuracy is checked by comparing the obtained solutions with semianalytical solutions through the well-known Adomian decomposition (AD) method. The superiority of the ERE method over the original method is explained. All constructed solutions are checked by submitting them back into the original model through Mathematica 12 software. (c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Automated summary

This article investigates novel soliton wave solutions of the nonlinear fractional ill-posed Boussinesq dynamic wave equation. The obtained solutions are explained in terms of their dynamic characteristics using the extended Riccati-expansion method, and their accuracy is verified by comparing them with semi-analytical solutions. The superiority of the extended Riccati-expansion method over the original method is discussed, and the solutions are further validated by submitting them back into the original model using Mathematica 12 software.