A class of integrable lattices and KP hierarchy

We introduce a class of integrable l-field first-order lattices together with corresponding Lax equations. These lattices may be represented as a consistency condition for auxiliary linear systems defined on sequences of formal dressing operators. This construction provides a simple way to build lattice Miura transformations between one-field lattice and l-field (l ≥ 2) ones. We show that the lattices pertained to by the above class are in some sense compatible with KP flows and define the chains of constrained Kadomtsev-Petviashvili Lax operators.