Pérez García, Victor M.. 

The method of moments in the context of nonlinear Schr¨odinger 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 us to get some approximate information on the dynamics of the solutions of the nonlinear Schr¨odinger equation.