An extended Painlevé integrable Kadomtsev--Petviashvili equation with lumps and multiple soliton solutions

Purpose This study aims to propose an extended (3 + 1)-dimensional integrable Kadomtsev–Petviashvili equation characterized by adding three new linear terms. Design/methodology/approach This study formally uses Painlevé test to confirm the integrability of the new system. Findings The Painlevé analysis shows that the compatibility condition for integrability does not die away by adding three new linear terms with distinct coefficients. Research limitations/implications This study uses the Hirota's bilinear method to explore multiple soliton solutions where phase shifts and phase variable are explored. Practical implications This study also furnishes a class of lump solutions (LSs), which are rationally localized in all directions in space, using distinct values of the parameters via using the positive quadratic function method. Social implications This study also shows the power of the simplified Hirota’s method in handling integrable equations. Originality/value This paper introduces an original work with newly developed Painlevé integrable model and shows new useful findings.