Lump-type solutions of a generalized Kadomtsev–Petviashvili equation in (3+1)-dimensions**Project supported by the National Natural Science Foundation of China (Grant Nos. 11505154, 11605156, 11775146, and 11975204), the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LQ16A010003 and LY19A050003), the China Scholarship Council (Grant No. 201708330479), the Foundation for Doctoral Program of Zhejiang Ocean University (Grant No. Q1511), the Natural Science

Abstract

Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions (or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.