Pfaffianized systems for a generalized Kadomtsev–Petviashvili equation

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. PACS numbers: 02.30.Ik, 02.90.+p

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