Nonlinear Impurity Modes in Homogeneous and Periodic Media

Details Nonlinear Impurity Modes in Homogeneous and Periodic Media Nonlinear Impurity Modes in Homogeneous and Periodic Media

2001-01-03

arxiv.org/abs/nlin/0101009v1

Nonlinear Sciences

Pattern Formation and Solitons

11 pages, 3 figures; To be published in: Proceedings of the NATO Advanced Research Workshop "Nonlinearity and Disorder: Theory

Scientific paper

We analyze the existence and stability of nonlinear localized waves described by the Kronig-Penney model with a nonlinear impurity. We study the properties of such waves in a homogeneous medium, and then analyze new effects introduced by periodicity of the medium parameters. In particular, we demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities associated with the band-gap wave resonances.

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