The moment method in general Nonlinear Schrodinger Equations

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.