Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

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dc.creatorSukhorukov, Andrey A.
dc.creatorKivshar, Yuri S.
dc.creatorBang, Ole
dc.creatorRasmussen, Jens J.
dc.creatorChristiansen, Peter L.
dc.date2000-09-03
dc.date.accessioned2026-07-07T05:32:59Z
dc.date.available2026-07-07T05:32:59Z
dc.descriptionWe 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.
dc.description18 pages, 22 figures
dc.identifierhttps://arxiv.org/abs/nlin/0009005
dc.identifierhttp://arxiv.org/abs/nlin/0009005
dc.identifierPhys. Rev. E 63, 036601(1-18) (2001)
dc.identifierdoi:10.1103/PhysRevE.63.036601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79854
dc.subjectPattern Formation and Solitons
dc.titleNonlinearity and disorder: Classification and stability of nonlinear impurity modes
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