  In this paper we develop a new approximation method valid for a wide family
of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a
reduced set of ordinary differential equations for a finite set of parameters
measuring global properties of the solutions, named momenta. We prove that
these equations provide exact results in some relevant cases and show how to
impose reasonable approximations that can be regarded as a perturbative
approach and as an extension of the time dependent variational method.
