Dynamic analysis and multiple solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

The localized wave solutions, the rogue wave solutions and interaction solutions of a (3+1)-dimensional generalized Kadomtsev–Petviashvili (GKP) equation were derived. These solutions corresponded to a total of eight sets of parameter relations. The test functions for the rogue wave solutions and the localized solutions were formed by the superposition of positive quadratic functions. Furthermore, the vector tool was specifically introduced in order to obtain the parameter relations in relation to solution functions expressed as superposition formulas. Dynamic analysis were performed on each type of solutions. The properties of all waves were exhibited through concrete examples and graphics.