In this paper, the invariant subspace classification of a class of nonlinear shallow water wave equation is given, then some exact explicit solutions to the nonlinear equation are provided by using the invariant subspace method. This method is a dynamical system method by nature, for its key step is to transform a nonlinear partial differential equation (PDE) into ordinary differential equation (ODE) systems, then by solving the ODE systems, the exact solutions to the nonlinear PDE are obtained.

中文翻译：

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一类非线性波动方程的不变子空间分类和精确解

本文给出了一类非线性浅水波方程的不变子空间分类，然后使用不变子空间方法为非线性方程提供了一些精确的显式解。该方法本质上是一种动力学系统方法，其关键步骤是将非线性偏微分方程（PDE）转换为常微分方程（ODE）系统，然后通过求解ODE系统，获得非线性PDE的精确解。 。