The "Ghost" Symmetry of the BKP hierarchy

Details The "Ghost" Symmetry of the BKP hierarchy The "Ghost" Symmetry of the BKP hierarchy

2010-03-31

arxiv.org/abs/1003.5987v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

23pages, to appear in Journal of Mathematical Physics

Scientific paper

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.

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