On a generalization of the KP hierarchy

The classical KP hierarchy can be defined and studied in terms of the ring of formal pseudodifferential operators and infinite-dimensional grassmanian manifolds. We will describe the ring of formal pseudodifferential operators for $n$ variables and will define an analogy of the KP hierarchy in that case. The talk contains a discussion of the hamiltonian structures, Baker–Akhieser and tau-functions related to this system.