The "Ghost" Symmetry of the BKP hierarchy
arXiv:1003.5987 · doi:10.1063/1.3397943
Abstract
In this paper, we systematically develop the "ghost" symmetry of the BKP hierarchy through its actions on the Lax operator $L$, the eigenfunctions and the $Ï$ function. In this process, the spectral representation of the eigenfunctions and a new potential are introduced by using squared eigenfunction potential(SEP) of the BKP hierarchy. Moreover, the bilinear identity of the constrained BKP hierarchy and Adler-Shiota-van-Moerbeke formula of the BKP hierarchy are re-derived compactly by means of the spectral representation and "ghost" symmetry.
23pages, to appear in Journal of Mathematical Physics