Spreading for the generalized nonlinear Schroedinger equation with disorder

The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |\psi|^p*\psi and "p" is arbitrary. Mainly short times for which the numerical calculations can be performed accurately are considered. Long time calculations are presented as well. In particular the subdiffusive behavior where the average second moment of the wavepacket is of the form <m_{2}>~t^a is computed. Contrary to former heuristic arguments, no evidence for any critical behavior as function of "p" is found. The properties of \alpha(t) are explored.