Nonlinearity and disorder: Classification and stability of nonlinear impurity modes | Zendy

Andrey A. Sukhorukov | Zendy; Yuri S. Kivshar | Zendy; Ole Bang | Zendy; J. Juul Rasmussen | Zendy; P. L. Christiansen | Zendy

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Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

Author(s) -

Andrey A. Sukhorukov,

Yuri S. Kivshar,

Ole Bang,

J. Juul Rasmussen,

P. L. Christiansen

Publication year - 2001

Publication title -

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Language(s) - English

Resource type - Journals

eISSN - 1095-3787

pISSN - 1063-651X

DOI - 10.1103/physreve.63.036601

Subject(s) - nonlinear system , impurity , instability , stability (learning theory) , physics , mode (computer interface) , statistical physics , condensed matter physics , quantum mechanics , computer science , machine learning , operating system

We study the effects produced by competition of two physical mechanisms ofenergy localization in inhomogeneous nonlinear systems. As an example, weanalyze spatially localized modes supported by a nonlinear impurity in thegeneralized nonlinear Schr\"odinger equation and describe three types ofnonlinear impurity modes --- one- and two-hump symmetric localized modes andasymmetric localized modes --- for both focusing and defocusing nonlinearityand two different (attractive or repulsive) types of impurity. We obtain ananalytical stability criterion for the nonlinear localized modes and considerthe case of a power-law nonlinearity in detail. We discuss several scenarios ofthe instability-induced dynamics of the nonlinear impurity modes, including themode decay or switching to a new stable state, and collapse at the impuritysite.Comment: 18 pages, 22 figure

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