Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N -soliton solutions are worked out, while two auto-Bäcklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N -soliton solutions and Bäcklund transformations are different from those in the existing literature. All of our results are dependent on the water-wave dispersive power.

中文翻译：

---

通过二重Bell多项式，N孤立子和Boussinesq-Burgers系统的Bäcklund变换的双线性形式，用于湖泊或海洋海滩中的浅水波

水波是自然界中最常见的现象之一，其研究有助于能源开发，海洋/海洋工程，水利工程，机械工程等。在此，对Boussinesq-Burgers系统中的浅水波进行符号计算湖泊或海洋海滩附近。对于水波的水平速度和底部上方水面的高度，通过二元Bell多项式和N-孤子解计算了两组双线性形式，同时构造了两个自动Bäcklund变换和孤子解，其中N是一个正整数。我们的双线性形式，N孤子解和Bäcklund变换与现有文献不同。我们所有的结果都取决于水波的分散能力。