The Lie-Poisson Hamiltonian Systems Associated With The 2+1 Dimensional DSI Equation

In this paper, the Lie-Poisson structure associated with the unitary algebra U(3) is given based on the Lie-Poisson structure of Lie algebra gl(3). Then under this structure, we study the finite dimensional Hamilton systems which are related to the 2+1 dimen-sional Davey-Stewartson I equation. By the characteristic polynomial of Lax matrix in this structure, we get 3N integral functions which are in involution with each other and functionally independent, then the integrability of the Hamilton systems in the sense of Liouville are proved.