Nonlinear localized waves resonance and interaction solutions of the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

This paper deals with localized waves in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in the incompressible fluid. Based on Hirota’s bilinear method, N -soliton solutions related to Boiti–Leon–Manna–Pempinelli equation are constructed. Novel nonlinear wave phenomena are obtained by selecting appropriate parameters to N -soliton solutions, and time evolutions of different kinds of solitary waves are investigated in detail. Rich elastic interactions are illustrated analytically and graphically. More specifically, the inelastic interactions, i.e., fusion and fission of solitary waves, are constructed by choosing special parameters on kink solitons and breathers. The analysis of the influence of parameters on propagation is revealed in three tables. The results have potential applications in fluid mechanics.