Water waves, one of the most common phenomena in nature, play an important role in the marine/offshore engineering, hydraulic engineering, energy development, mechanical engineering, etc. Hereby, for the shallow water waves near an ocean beach or in a lake, we study a Boussinesq-Burgers system. With respect to the water-wave horizontal velocity and height deviating from the equilibrium position of water, we find out (1) two hetero-Bäcklund transformations via the Bell polynomials and symbolic computation, and (2) a set of the similarity reductions via symbolic computation, to a known ordinary differential equation, for which we also construct some solutions. The results rely on the oceanic water-wave dispersive power. We hope that our hetero-Bäcklund transformations and similarity reductions could help the researchers investigate certain modes of the shallow water waves near an ocean beach.

水波是自然界中最常见的现象之一，在海洋/海洋工程，水利工程，能源开发，机械工程等方面发挥着重要作用。因此，对于海洋沙滩或湖泊附近的浅水波，我们研究了Boussinesq-Burgers系统。关于偏离水的平衡位置的水波水平速度和高度，我们发现（1）通过Bell多项式和符号计算的两个异质Bäcklund变换，以及（2）通过符号简化的一组相似性约简计算已知的常微分方程，为此我们还构造了一些解。结果依赖于海洋水波的分散能力。