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

Abstract

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.

Keywords:

• Complete discrimination system for polynomial method
• shallow water wave equation
• Hamiltonian
• qualitative analysis
• quantitative analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China under Grant No. 62072296.