Anderson localization in the quintic nonlinear Schr\"odinger equation

In the present paper we consider the quintic defocusing nonlinear Schr\"odinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The main result shows that Anderson localization requires a cutoff on the value of the parameter which controls the quintic nonlinearity, with the cutoff depending on the amplitude of the random potential.