  The method of moments in the context of Nonlinear Schrodinger Equations
relies on defining a set of integral quantities, which characterize the
solution of this partial differential equation and whose evolution can be
obtained from a set of ordinary differential equations. In this paper we find
all cases in which the method of moments leads to closed evolution equations,
thus extending and unifying previous works in the field of applications. For
some cases in which the method fails to provide rigorous information we also
develop approximate methods based on it, which allow to get some approximate
information on the dynamics of the solutions of the Nonlinear Schrodinger
equation.
