Surface gravity waves of the Boussinesq equation

TL;DR

This paper presents exact solutions to the Boussinesq equation using Hirota's method, revealing complex wave structures like solitons and wave packets in shallow water modeling.

Contribution

It introduces a simple multiplication method for Hirota solutions, enabling the generation of complex wave structures in shallow water wave models.

Findings

Exact solutions describe wave packets and solitons

Method for multiplying solutions creates complex wave patterns

Solutions illustrate diverse wave phenomena in shallow water

Abstract

This article is devoted to exact solutions of the Boussinesq equation that models nonlinear shallow water waves. For this we use the Hirota bilinear method and differential constrains. Out solutions describe in particular the motion of the wave packets, waves on soliton and "dancing" waves. We present a simple method for multiplication of solutions of the Hirota equation which allow us to generate more complex structures from the waves.