@article{Khater2022, 
author = {Mostafa M. A. Khater and S. H. Alfalqi and J. F. Alzaidi and Samir A. Salama and Fuzhang Wang},
title = {Plenty of wave solutions to the ill-posed Boussinesq dynamic wave equation under shallow water beneath gravity},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {54-81},
keywords = {ill-posed Boussinesq dynamical wave, extended simple equation (ESE) method, novel Riccati expansion (NRE) method, nonlinear soliton lattice wave solutions},
url = {https://www.sciopen.com/article/10.3934/math.2022004},
doi = {10.3934/math.2022004},
abstract = {This paper applies two computational techniques for constructing novel solitary wave solutions of the ill-posed Boussinesq dynamic wave (IPB) equation. Jacques Hadamard has formulated this model for studying the dynamic behavior of waves in shallow water under gravity. Extended simple equation (ESE) method and novel Riccati expansion (NRE) method have been applied to the investigated model's converted nonlinear ordinary differential equation through the wave transformation. As a result of this research, many solitary wave solutions have been obtained and represented in different figures in two-dimensional, three-dimensional, and density plots. The explanation of the methods used shows their dynamics and effectiveness in dealing with certain nonlinear evolution equations.}
}