Abstract: In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.

Key words: heat conduction, nonlinear, similar solution, infinite dimension dynamics system, nonlinear Schfrodingerequation, indefinite metric space, dissipative operator