LAUSR

Interaction solutions are obtained from (2+1)-dimensional BLMP equation and (3+1)-dimensional nonlinear evolution equation by using a direct method. The interaction solutions of the two equations presented that a lump appear from a soliton wave and swallowed by it later, they are all the completely non-elastic interactions that rare to see. It shows that a lump appeared from the one side of the soliton wave (a kinky wave or another solitary wave), and separate slowly from this side of the soliton wave, after reaching the maximum separation at $$t=0,$$t=0, the lump gradually walks upon the other side of the soliton wave and finally swallowed by the other side. The dynamical character shows in this work enriches the variety of the dynamics of higher-dimensional nonlinear wave field.