Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrödinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discrete model, the disorder is found to leave the narrow excitations unaffected. Our results suggest that the disorder provides a possibility to control the spatial extent of the stable excitations in the continuum system.