In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained. Their interaction phenomena is shown in some 3d graphs and contour plots, which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution,interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented.

中文翻译：

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含气泡液体中广义(3+1)维变系数非线性波动方程的团波与孤波相互作用现象

本文研究了含气泡液体中的广义(3+1)维变系数非线性波动方程。基于Hirota的双线性形式和符号计算，获得了块和孤波之间的块和相互作用解。它们的相互作用现象显示在一些 3d 图形和等高线图中，包括周期形状的块解、抛物线形的块解、立方体的块解、块和一个孤立波之间的相互作用解、块和两个之间的相互作用解。孤波。讨论了称为亮团波和亮暗团波的空间结构。还介绍了两个亮暗团波和一个周期形状的亮团波的相互作用。