Four (2 + 1)-dimensional integrable extensions of the Kadomtsev–Petviashvili equation

In this work, four (2 + 1)-dimensional nonlinear extensions of the Kadomtsev–Petviashvili (KP) equation are developed. The complete integrability of these models are investigated. Multiple-soliton solutions and multiple singular soliton solutions are determined to demonstrate the compatibility of these models. The resonance phenomenon does not exist for any of the derived models.