A study of the shallow water waves with some Boussinesq-type equations

In this paper, analytic solutions and dynamic properties of a variety of Boussinesq-type equations are established via the complete discrimination system for polynomial method. All the existing single traveling wave solutions to these equations as well as some new solutions are shown, and the Hamiltonian and topological properties to these equations are also presented. Considering the significance of the Boussinesq-type equations, our results would have wide applications in ocean engineering and fluid mechanics, like describing and predicting the solitary and periodic waves in various shallow water models.

Automated summary

This paper establishes analytic solutions and dynamic properties of a variety of Boussinesq-type equations through the complete discrimination system for polynomial method. It shows existing single traveling wave solutions to these equations as well as new solutions, and presents the Hamiltonian and topological properties of these equations. The significance of the Boussinesq-type equations lies in their wide applications in ocean engineering and fluid mechanics, especially in describing and predicting solitary and periodic waves in various shallow water models.