Painleve integrability and lump solutions for two extended (3+1)- and (2+1)-dimensional Kadomtsev-Petviashvili equations

The current work introduces two extended (3 + 1)- and (2 + 1)-dimensional Painleve integrable Kadomtsev-Petviashvili (KP) equations. The integrability feature of both extended equations is carried out by using the Painleve test. We use the Hirota's bilinear strategy to explore multiple-soliton solutions for both extended models. Moreover, we formally furnish a class of lump solutions, for each extended KP equation, by using distinct values of the parameters. Proper graphs are furnished to highlight the characteristics of the lump, contour, and density solutions.