Nonlinearity and disorder: Classification and stability of nonlinear impurity modes - art. no. 036601

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we a nalyze spatially localized modes supported by a nonlinear impurity in the g eneralized nonlinear Schrodinger equation and describe three types of nonli near impurity modes, one- and two-hump symmetric localized modes and asymme tric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analyt ical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios o f the instability-induced dynamics of the nonlinear impurity modes, includi ng the mode decay or switching to a new stable state, and collapse at the i mpurity site.