Darboux Coverings and Rational Reductions of the KP Hierarchy


We use the method of Darboux coverings to discuss the invariant submanifolds of the KP equations, presented as conservation laws in the space of monic Laurent series in the spectral parameter (the space of the Hamiltonian densities). We identify a special class of these submanifolds with the rational invariant submanifolds entering matrix models of 2D–gravity, recently characterized by Dickey and Krichever. Four examples of the general procedure are provided. Work supported by the Italian M.U.R.S.T. and by the G.N.F.M. of the Italian C.N.R

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@inproceedings{Casati1996DarbouxCA, title={Darboux Coverings and Rational Reductions of the KP Hierarchy}, author={Paolo Casati and Gregorio Falqui and Franco Magri and Marco Pedroni}, year={1996} }