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

Spreading for the generalized nonlinear Schroedinger equation with disorder