Considering the water waves, people have investigated many systems. In this paper, what we study is a Whitham-Broer-Kaup-like system for the dispersive long waves in the shallow water in an ocean. With respect to the water-wave horizontal velocity and deviation height from the equilibrium of the water, we construct (A) two branches of the hetero-Bäcklund transformations, from that system to a known constant-coefficient nonlinear dispersive-wave system, (B) two branches of the bilinear forms and (C) two branches of the $M$-soliton solutions, with $M$ as a positive integer. Results rely upon the oceanic shallow-water coefficients in that system.

中文翻译：

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关于通过 Whitham-Broer-Kaup 类系统在海洋中的浅水：hetero-Bäcklund 变换、双线性形式和 M 孤子

考虑到水波，人们研究了许多系统。在本文中，我们研究的是一个类 Whitham-Broer-Kaup 系统，用于海洋浅水中的色散长波。关于水波水平速度和偏离水平衡的高度，我们构建了（A）异质贝克伦变换的两个分支，从该系统到已知的恒定系数非线性色散波系统，（B ) 双线性形式的两个分支和 (C) 的两个分支$米$-孤子解决方案，与$米$作为一个正整数。结果依赖于该系统中的海洋浅水系数。