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Nonlinear Impurity Modes in Homogeneous and Periodic Media
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.Comment: 11 pages, 3 figures; To be published in: Proceedings of the NATO
Advanced Research Workshop "Nonlinearity and Disorder: Theory and
Applications" (Tashkent, 2-6 Oct, 2000) Editors: P.L. Christiansen and F.K.
Abdullaev (Kluwer, 2001