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

Abstract

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 semi-analytical 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.