In this paper, the resonant solitary waves to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations are exposed via the simplified linear superposition principle (LSP). Based on the related Hirota’s bilinear equations, the resonant multi-soliton solutions and the corresponding wave numbers are formally generated. Abundant inelastic interactions, i.e., fission and fusion of traveling N-solitary waves, are presented analytically and graphically. Besides, we show that the velocity resonance (VR) is not applicable to handle the (3 + 1)- and (4 + 1)-dimensional BLMP equations, due to that the dispersion relation is constructed as \(\omega = - k^{3}\). The results show that the simplified LSP provides enough freedom to construct resonant multi-soliton waves that has potential applications to a large variety of real physical phenomena.

在本文中，通过简化的线性叠加原理（LSP）暴露了（3 +1）维和（4 +1）维Boiti-Leon-Manna-Pempinelli（BLMP）方程的共振孤波。基于相关的Hirota双线性方程，正式生成了共振多孤子解和相应的波数。分析和图形显示了丰富的非弹性相互作用，即行进的N孤立波的裂变和融合。此外，由于色散关系构造为\（\ omega =-k，因此，我们表明速度共振（VR）不适用于处理（3 +1）-和（4 +1）维BLMP方程。^ {3} \）。结果表明，简化的LSP提供了足够的自由来构造共振多孤子波，该波对许多实际物理现象都有潜在的应用。