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Instabilities and Bifurcations of Nonlinear Impurity Modes

Panayotis G. Kevrekidis·Yuri S. Kivshar·Alexander S. Kovalev
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Abstract

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{ö}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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Panayotis G. Kevrekidis, Yuri S. Kivshar, Alexander S. Kovalev. 2003-02-05. Instabilities and Bifurcations of Nonlinear Impurity Modes. https://doi.org/10.1103/physreve.67.046604

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