Study of three integrable extensions of Kadomtsev―Petviashvili, Boussinesq, and Kadomtsev―Petviashvili―Boussinesq equations

We study three (2 + 1)-dimensional extensions of Kadomtsev–Petviashvili (eKP) equation, Boussinesq (eBO) equation, and Kadomtsev–PetviashviliBoussinesq (eKP-eBO) equation that appear in many physical settings in dissipative media. The Painleve test is employed to confirm the integrability of each proposed ´ model. We furnish dispersion relations, phase shifts, and multiple soliton solutions for each extended model. The bilinear form of each equation will be used to explore a class of lump solutions for these equations using distinct values of the parameters.