  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.
