Soliton molecules and the novel hybrid interaction solutions of the new extended (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

The current work is concerned with some novel solutions of the new extended (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation (BLMPE) that plays a key role in the incompressible fluid. The N-soliton solutions (NSSs) are extracted by virtue of the Hirota form which is developed using the Cole–Hopf transform. Based on the NSSs, we elaborate the resonance conditions of the soliton molecules and derive the soliton molecules of the 2-solitons, 3-solitons and 4-solitons on the (x, y)-, (x, z)- and (y, z)-planes. Additionally, we also explore some novel hybrid interaction solutions including the interaction between the soliton molecule and solitons and the interaction between the breather solution and the solitons. Correspondingly, the dynamic properties of the solutions are depicted graphically. The derived solutions in this study are all new and can enlarge the exact solutions of the new extended (3 + 1)-dimensional BLMPE. Besides, they can enable us to understand nonlinear dynamic behaviours better.