Novel resonant multi-soliton solutions and inelastic interactions to the (3+1)- and (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equations via the simplified linear superposition principle

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.