Analytical solution for Solitary wave using extended Boussinesq equations of Madsen and Sørensen

Abstract

In this paper, the author introduces an analytical solution for the solitary wave using the extended Boussinesq equations developed by Madsen and Sørensen in 1992. The solution is derived using a mathematical method, where the potential velocity is applied to the Boussinesq equations, resulting in analytical solutions for water surface elevation and horizontal particle velocity. The analytical solution is applied as an initial condition for the simulation of tsunami or solitary waves. The solitary wave is a crucial physical feature of many natural systems, such as ocean waves, and is characterized as a wave that retains its shape and height as it travels over long distances. To validate the proposed solution, the author compares the numerical results of the derived analytical solution with those of other solutions and finds a high degree of accuracy. The findings of this study contribute to a better understanding of the dynamics of solitary waves and provide a useful tool for the numerical simulation of water waves using the extended Boussinesq equations of Madsen and Sørensen.