Instabilities and Bifurcations of Nonlinear Impurity Modes

Details Instabilities and Bifurcations of Nonlinear Impurity Modes Instabilities and Bifurcations of Nonlinear Impurity Modes

2003-02-05

arxiv.org/abs/nlin/0302010v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 8 figures, Phys. Rev. E in press

Scientific paper

10.1103/PhysRevE.67.046604

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 transition between different localized states via a cascade of bifurcations.

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