A New ``Dual'' Symmetry Structure of the KP Hierarchy

Details A New ``Dual'' Symmetry Structure of the KP Hierarchy A New ``Dual'' Symmetry Structure of the KP Hierarchy

1997-12-18

arxiv.org/abs/solv-int/9712012v2

Physics

High Energy Physics

High Energy Physics - Theory

Added one reference, LaTeX, 8 pgs

Scientific paper

10.1016/S0375-9601(98)00340-5

A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding ``ghost'' and original KP-type Lax hierarchies connected to each other via a ``duality'' mapping exchanging the isospectral and ``ghost'' ``times''. A new representation of 2D Toda lattice hierarchy as a special Darboux-Backlund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eigenfunctions of the original KP subsystem.

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