Pfaffianization of the generalized variable-coefficient Kadomtsev–Petviashvili equation

In this paper, the pfaffianization procedure is applied to the generalized variable-coefficient Kadomtsev–Petviashvili (vcKP) equation which can describe the realistic nonlinear phenomena in the fluid dynamics and plasmas. Using the pfaffianization procedure, the coupled system for the generalized vcKP equation is derived together with the Wronski-type pfaffian solution for this generalized coupled vcKP system under certain coefficient constraint. Furthermore, the Gramm-type pfaffian solution for such a coupled system is presented and verified by virtue of the pfaffian identities.