We study the affinities between the shape of the bright soliton of the
one-dimensional nonlinear Schroedinger equation and that of the disorder
induced localization in the presence of a Gaussian random potential. With
emphasis on the focusing nonlinearity, we consider the bound states of the
nonlinear Schroedinger equation with a random potential; for the state
exhibiting the highest degree of localization, we derive explicit expressions
for the nonlinear eigenvalue and for the localization length by using
perturbation theory and a variational approach following the methods of
statistical mechanics of disordered systems. We numerically investigate the
linear stability and "superlocalizations". The profile of the disorder averaged
Anderson localization is found to obey a nonlocal nonlinear Schroedinger
equationComment: 5 pages, 3 figure
