Waves are seen in the atmosphere, oceans, etc. As one of the most common natural phenomena, water waves attract the attention of researchers. For the shallow water waves, a (3+1)-dimensional generalized nonlinear evolution equation is hereby investigated via the symbolic computation. Based on the Hirota method, we present three bilinear auto-Bäcklund transformations, along with some soliton solutions. Our results depend on the water-wave coefficients in that equation.

中文翻译：

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浅水波(3+1)维广义非线性演化方程的双线性自Bäcklund变换和孤子解

在大气、海洋等中可以看到波浪。作为最常见的自然现象之一，水波引起了研究人员的注意。对于浅水波，通过符号计算研究了一个(3+1)维广义非线性演化方程。基于 Hirota 方法，我们提出了三个双线性 auto-Bäcklund 变换，以及一些孤子解决方案。我们的结果取决于该方程中的水波系数。