In this study, we focus on the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which is useful for modeling weakly dispersive waves transmitted in quasi media and fluid mechanics.As a general matter, this paper examines the gBKP equation including variable coefficients of time that are widely employed in machine-accessories plasma physics, marine engineering, ocean physics, and nonlinear sciences to explain shallow water waves.Using Hirota’s bilinear approach, one-, two, and three-soliton solutions to the problem are constructed.By employing a long-wave method, 1-M-, 2-M, and 3-M-lump solutions are derived.
In addition, interaction phenomena of one-, and two-soliton solutions with one-M-lump wave are revealed.Moreover, an interaction solution Hand Lotion between a two-M-lump wave and a one-soliton solution is also offered.The planes that M-lump waves travel among them are derived.We believe that our findings will help improve the dynamical properties of (3+1)-dimensional BKP-type equation.