A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves

Abstract

In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlevé analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method, a symbolic computation scheme. Furthermore, the abundant dynamical behaviors for these solutions are discovered. It is interesting that there are splitting and fusing phenomena when the lump waves interact. The results can well simulate complex waves and their interaction dynamics in fluids.