Abstract
We first introduce a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like (KPB-like) equation. In order to study the dynamics of lump solutions of this new model, two dimensionally reduced cases are firstly investigated by using the generalized bilinear method. The quadratic functions are used to construct lump solutions to the aforementioned dimensionally reduced cases. Analyzing these lumps, we find the free parameters play an important role during the research on the dynamics of lump solutions, which are utilized to find the sufficient and necessary conditions for guaranteeing the existence, the analyticity and the rational localization of lump solitary waves. The triple sums of quadratic function solutions are further studied. To show the dynamics, we present some graphical analyses of the resulting solutions, which can be applied to the study of nonlinear phenomena in physics, such as nonlinear optics, and oceanography.