The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in (3 + 1)-dimensions

By applying the Painlevé test, the Kadomtsev–Petviashvili equation and Jimbo–Miwa equation in (3 + 1)-dimensions are shown to be non-integrable. Through the obtained truncated Painlevé expansions, two bilinear equations are constructed. In addition, starting from the bilinear equations, one soliton, two soliton and dromion solutions are also derived. The analysis of the dromions shows that the interactions of the dromions for the (3 + 1)-dimensional equations may be elastic or inelastic.