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.

中文翻译：

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浅水波的一些Boussinesq型方程研究

本文通过多项式方法的完全判别系统建立了多种Boussinesq型方程的解析解和动力学性质。显示了这些方程的所有现有单行波解以及一些新解，并且还给出了这些方程的哈密顿量和拓扑性质。考虑到 Boussinesq 型方程的重要性，我们的结果将在海洋工程和流体力学中具有广泛的应用，例如描述和预测各种浅水模型中的孤立波和周期波。