  Invariant submanifolds of the so-called Darboux-KP chain are investigated. It
is shown that restriction of dynamics on some class of invariant submanifolds
yields the extension of the discrete KP hierarchy, while the intersections
leads to Lax pairs for a broad class of differential-difference systems with
finite number of fields. Some attention is given to investigation of
self-similar reductions. It is shown that self-similar ansatzes lead to purely
discrete equations with dependence on some number of parameters together with
equations governing deformations with respect to these parameters. Some
examples are provided. In particular it is shown that well known first discrete
Painleve equation (dPI) corresponds to Volterra lattice hierarchy. It is
written down equations which naturally generalize dPI in the sense that they
have first Painleve transcedent in continuous limit.
