Ghost symmetry of the discrete KP hierarchy

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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17 pages

Scientific paper

In this paper, we define the $S$ function, $H$ function and ghost symmetry for the discrete KP hierarchy. By spectral representation of Baker-Akhiezer function and adjoint Baker-Akhiezer function, we derive ghost flow of eigenfunction and adjoint eigenfunction. Also we give ghost flow on tau function and another kind of proof of ASvM formula of the discrete KP hierarchy. From these observations above, some important distinctions between the discrete KP hierarchy and KP hierarchy are shown. These distinctions in fact give the effect of discretization from KP hierarchy to the discrete KP hierarchy.

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