Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy

Abstract

An extension of the Kadomtsev-Petviashvili (KP) hierarchy was considered in [J. Geom. Phys. 106 (2016), 327--341], which possesses a class of bi-Hamiltonian structures. In this paper, we represent the extended KP hierarchy into the form of bilinear equation of (adjoint) Baker-Akhiezer functions, and construct its additional symmetries. As a byproduct, we also derive the Virasoro symmetries for the constrained KP hierarchies.