Incompressible fluids are studied in such disciplines as ocean engineering, astrophysics and aerodynamics. Under investigation in this paper is a (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in an incompressible fluid. Based on the known bilinear form, BLMP hybrid solutions comprising a lump wave, a periodic wave and two kink waves, and hybrid solutions comprising a breather wave and multi-kink waves are derived. We observe the interaction among a lump wave, a periodic wave and two kink waves. Fission of a kink wave is observed: A kink wave divides into a breather wave and three kink waves. On the contrary, we see the fusion among a breather wave and three kink waves: The breather wave and three kink waves merge into a kink wave. Finally, we observe the interaction among a breather wave and four kink waves.

中文翻译：

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(3 + 1) 维 Boiti–Leon–Manna–Pempinelli 方程在不可压缩流体中的混合解

在海洋工程、天体物理学和空气动力学等学科中研究不可压缩流体。本文研究的是一个(3 + 1)不可压缩流体中的维 Boiti-Leon-Manna-Pempinelli (BLMP) 方程。基于已知的双线性形式，推导出包括一个团波、一个周期波和两个扭结波的BLMP混合解，以及包括一个呼吸波和多个扭结波的混合解。我们观察到一个团波、一个周期波和两个扭结波之间的相互作用。观察到扭结波的裂变：扭结波分为呼吸波和三个扭结波。相反，我们看到一个呼吸波和三个扭结波之间的融合：呼吸波和三个扭结波合并成一个扭结波。最后，我们观察到一个呼吸波和四个扭结波之间的相互作用。