title: Instabilities and bifurcations of nonlinear impurity modes.
abstract: We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schrödinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity, and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors.forename: Panayotis G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: Yuri S
authors.initials: YS
authors.lastname: Kivshar
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Kovalev