A New ``Dual'' Symmetry Structure of the KP Hierarchy
solv-int
2009-10-30 v2 High Energy Physics - Theory
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.solv-int/9712012,
title = {A New ``Dual'' Symmetry Structure of the KP Hierarchy},
author = {H. Aratyn and E. Nissimov and S. Pacheva},
journal= {arXiv preprint arXiv:solv-int/9712012},
year = {2009}
}
Comments
Added one reference, LaTeX, 8 pgs