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In this paper, we construct the bilinear identities for the wave functions ofan extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchywith particular extended flows (2008, Phys. Lett. A, 372: 3819). By introducingan auxiliary parameter (denoted by $z$), whose flow corresponds to theso-called squared eigenfunction symmetry of KP hierarchy, we find thetau-function for this extended KP hierarchy. It is shown that the bilinearidentities will generate all the Hirota's bilinear equations for thezero-curvature forms of the extended KP hierarchy, which includes two types ofKP equation with self-consistent sources (KPSCS). It seems that the Hirota'sbilinear equations obtained in this paper for KPSCS are in a simpler form bycomparing with the results by Hu and Wang (2007, Inverse Problems, 23: 1433).

Bilinear Identities and Hirota's Bilinear Forms for an Extended Kadomtsev-Petviashvili Hierarchy