New extended Kadomtsev–Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions

In this paper, we develop a new extended Kadomtsev–Petviashvili (eKP) equation. We use the Painlevé analysis to confirm the integrability of the eKP equation. We derive the bilinear form, multiple soliton solutions and lump solutions via using the Hirota’s direct method. Moreover, the soliton, breather and lump interaction solutions for this model are also obtained as well. Graphs are drawn to illustrate the abundant dynamical behaviors of the obtained solutions.