In this paper, the extended (3+1)-dimensional potential KP equation in fluid mechanics is studied through Hirota bilinear method. Many types of hybrid solutions, such as the lump–kink solution, lump-two kink solution and periodic lump solution are obtained by assuming different functions in the bilinear equation. The interaction solution between lump and triangular periodic wave is also derived by combining sine and cosine functions with quadratic functions. Dynamical structures of these exact solutions are depicted by presenting the corresponding three-dimensional, two-dimensional structures and density graphs. These diverse interaction solutions could be helpful for understanding physical phenomena in fluid mechanics.

本文通过Hirota双线性方法研究了流体力学中扩展的(3+1)维势KP方程。通过假设双线性方程中的不同函数，可以得到许多类型的混合解，例如块-扭结解、块-二扭结解和周期块解。还通过将正弦、余弦函数与二次函数相结合，导出了块波和三角周期波之间的相互作用解。通过呈现相应的三维、二维结构和密度图来描述这些精确解的动态结构。这些不同的相互作用解决方案可能有助于理解流体力学中的物理现象。