Darboux Coverings and Rational Reductions of the KP Hierarchy

1996/10/01 by Paolo Casati, Gregorio Falqui, Casati, Paolo +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9610002

16 pages, LaTeX

arxiv created 1996/10/01 · arxiv updated 2009/11/30

Abstract

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.

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