Nonlinear generalization of Mori's method of projection operators

Mori's technique of projection operators is used as the basis for a consistent separation from the microscopic expressions of secular contributions associated with the densities of conserved quantities. Additional conserved quantities that are quadratic combinations of the ordinary hydrodynamic variables are added to Mori's scheme. This makes it possible to go beyond linear processes. In contrast to Kawasaki's equations, the results obtained here agree with ordinary linear hydrodynamics. Boundary conditions of retarded type are introduced into Mori's equations, which render them translationally invariant with respect to the time.