The "ghost" symmetry of the BKP hierarchy

Abstract

In this paper, we systematically develop the "ghost" symmetry of the Kadomtsev-Petviashvili sub-hierarchy of B type (BKP) through its actions on the Lax operator L, the eigenfunctions, and the τ function. In this process, the spectral representation of the eigenfunctions and a new potential are introduced by using squared eigenfunction potential of the BKP hierarchy. Moreover, the bilinear identity of the constrained BKP hierarchy and Adler-Shiota-van Moerbeke formula of the BKP hierarchy are rederived compactly by means of the spectral representation and "ghost" symmetry. © 2010 American Institute of Physics.