Interaction of localized waves and dynamic behavior in a (3 + 1)-dimensional partial differential equation

A general third order of linear partial differential equation in [Formula: see text] dimensions is studied by using the ansätz method. The lump solutions which localize in all directions in the whole [Formula: see text]-space are derived by the ansätz method. Diversity interactions including interacted lumps with periodic waves, interaction between lumps and multi-soliton, and interaction among lumps, multi-soliton and periodic waves are obtained by selecting the arbitrary functions. The phenomena of interaction between a lump and one-kink soliton, interaction between a lump and periodic waves, and interaction among a lump, one-kink soliton and periodic waves are analyzed by the three-dimensional plots and contour plots. The results may enrich the existing lump solutions in the [Formula: see text]-dimensional partial differential equations.