New Painlevé integrable (3+1)-dimensional combined pKP–BKP equation: Lump and multiple soliton solutions

Abstract We introduce a new Painlevé integrable (3+1)-dimensional combined potential KadomtsevPetviashvili equation with B-type Kadomtsev-Petviashvili equation, that will be called pKP-BKP equation. We perform the Painlevé analysis to emphasize the complete integrability of this newly (3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota’s bilinear method. Moreover, a variety of lump solutions will be determined. We also develop two new (3+1)-dimensional pKP-BKP equations via deleting some terms from the original form of the combined pKP-BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions were derived as well. The derived solutions for all examined models are all depicted through the Maple software.