Solitons and disorder-induced Anderson states are two apparently unrelated forms of wave localization, the former being due to nonlinearity and the latter to linear disorder.
However, on closer inspection, solitons and disorder induced localized states have similarities: exponential localization, negative eigenvalues, any possible position in space. In the presence of nonlinearity, disorder-induced localizations are expected to have eigenvalue and localization length dependent on power. These states, however, also exist for a negligible nonlinearity: Hence, in the low fluence regime, they are linear Anderson localizations, but at high fluence, they become related to solitons.
In Physical Review A, we analytically and numerically study the process of “solitonization of the Anderson localization,” that is smooth transition from disorder induced to nonlinearity induced wave localization in random media.