Instabilities and bifurcations of nonlinear impurity modes

Panayotis G. Kevrekidis, Yuri S. Kivshar, Alexander S. Kovalev
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger 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
more » ... al criteria for the transition between different localized states via a cascade of bifurcations.
doi:10.1103/physreve.67.046604 pmid:12786506 fatcat:2ojkkaavsfa3lc6y4kkqs2pwy4