The "Ghost" Symmetry of the BKP hierarchy

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 $\tau$ 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

References in corpus (2)

• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• On the String Equation of the BKP Hierarchy

Cited by in corpus (10)

• Supersymmetric BKP systems and their symmetries
• Bilinear equations in Darboux transformations by Boson-Fermion correspondence
• The "ghost" symmetry in the CKP hierarchy
• Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy
• On the squared eigenfunction symmetry of the Toda lattice hierarchy
• Bilinear identities for an extended B-type Kadomtsev-Petviashvili hierarchy
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies
• The Recursion operators of the BKP hierarchy and the CKP Hierarchy
• The applications of the gauge transformation for the BKP hierarchy