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

In this paper, a new (3+1)-dimensional integrable Kadomtsev-Petviashvili equation is developed. Its integrability is verified by the Painleve 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. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents a new (3+1)-dimensional integrable Kadomtsev-Petviashvili equation, whose integrability is confirmed through Painleve analysis. Various solutions including bilinear form, multiple-soliton, breather, and lump solutions are obtained using the Hirota bilinear method, revealing rich dynamical behaviors. Notably, splitting and fusing phenomena are observed when lump waves interact, offering insights into complex wave dynamics in fluids.