Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

Andrey A. Sukhorukov, Yuri S. Kivshar, Ole Bang, Jens Juul Rasmussen, Peter Leth Christiansen

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    Abstract

    We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume63
    Issue number3
    Pages (from-to)036601.1 - 036601.18
    ISSN1063-651X
    DOIs
    Publication statusPublished - 2001

    Bibliographical note

    Copyright (2001) American Physical Society

    Keywords

    • PHOTONIC CRYSTALS
    • COLLAPSE
    • WAVE-GUIDE ARRAYS
    • SCATTERING
    • INTERFACE
    • SCHRODINGER-EQUATION
    • LOCALIZED MODES
    • SOLITONS
    • LINEAR-CHAIN
    • SOLITARY WAVES

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