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

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