Pfaffianized systems for a generalized Kadomtsev-Petviashvili equation

Abstract

A one-parameter class of Pfaffian extensions is made for a (3 + 1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation by the Pfaffianization procedure. Wronski-type Pfaffian and Gramm-type Pfaffian solutions of the resulting Pfaffianized bilinear systems of the generalized KP equation are constructed. Under a dimensional reduction, our results yield a class of Pfaffianized bilinear systems for the KP equation, which contains the standard Pfaffianized bilinear KP system as a particular example. Two kinds of Pfaffian identities provide the basis for our analysis. © 2013 The Royal Swedish Academy of Sciences.