Multiple-lump waves for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation arising from incompressible fluid

A (3+1)-dimensional Boiti–Boiti–Leon–Manna– Pempinelli equation is investigated, which describes nonlinear wave propagations in incompressible fluid. A condition proposition is obtained for polynomial function in bilinear form. New lump solution is constructed by applying the bilinear method and choosing proper polynomial function. Under different parameter settings, this lump solution possesses three types of multiple-lump waves, namely, two-, four- and eight-lump waves. Mixed solutions involving lump waves and solitons are also constructed. Interaction behaviors are observed between lump soliton and soliton. Research shows that soliton can partially swallow or spit out lump waves. Furthermore, number of lump wave peaks will change with time.