Wronskian solutions and Pfaffianization for a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma

In this paper, we investigate a (3 + 1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma. The Nth-order Wronskian solutions for that equation are derived and proved under certain variable-coefficient constraints, where N is a positive integer. One-, two-, and three-soliton solutions in the Wronskian for that equation are given. By means of the Pfaffianization procedure, a coupled (3 + 1)-dimensional GVCKP system is constructed from that equation. Bilinear form for that coupled system is exported. Under certain variable-coefficient constraints, those Wronski-type and Gramm-type Pfaffian solutions for that coupled system are obtained and proved with the help of the Pfaffian identities.

Automated summary

In this paper, a (3 + 1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma is investigated. The Nth-order Wronskian solutions for that equation are derived and proved under certain variable-coefficient constraints, where N is a positive integer. One-, two-, and three-soliton solutions in the Wronskian for that equation are given. By means of the Pfaffianization procedure, a coupled (3 + 1)-dimensional GVCKP system is constructed from that equation. Bilinear form for that coupled system is exported. Under certain variable-coefficient constraints, those Wronski-type and Gramm-type Pfaffian solutions for that coupled system are obtained and proved with the help of the Pfaffian identities.