Painlev\'{e} integrability, B\"{a}cklund transformations and Wronskian solutions for a (2+1)-dimensional combined potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics

Abstract

In this paper, we investigate a (2+1)-dimensional combined potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics.Painlevé integrability is confirmed under certain coefficient constraint. Using the truncated Painlevé expansion, two auto-Bäcklund transformations with the kink-soliton solutions are derived. Based on the Wronskian technique, two cases of the Nth-order Wronskian solutions are constructed and proved, where N is a positive integer. One-, two-, and three-soliton solutions in the Wronskian are given.