Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

Andrey A. Sukhorukov; Yuri S. Kivshar; Ole Bang; Jens J. Rasmussen; Peter L. Christiansen

doi:10.1103/PhysRevE.63.036601

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

Andrey A. Sukhorukov, Yuri S. Kivshar, Ole Bang, Jens J. Rasmussen, Peter L. Christiansen

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

Abstract

Spatially localized nonlinear modes supported by a pointlike impurity, in the framework of the generalized nonlinear Schrodinger (NLS) equation were analyzed. Three possible types of such nonlinear impurity modes were considered, symmetric one- and two-hump modes and asymmetric one-hump mode. Their regions of existence and stability for both focusing and defocusing nonlinearity of a bulk medium and two different types of the impurity. An analytical stability criterion for nonlinear localized modes based on the results of the linear stability analysis of the generalized NLS equation was obtained.

Original language	English
Article number	036601
Pages (from-to)	366011-3660118
Number of pages	3294108
Journal	Physical Review E
Volume	63
Issue number	3 II
DOIs	https://doi.org/10.1103/PhysRevE.63.036601
Publication status	Published - Mar 2001

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abstract = "Spatially localized nonlinear modes supported by a pointlike impurity, in the framework of the generalized nonlinear Schrodinger (NLS) equation were analyzed. Three possible types of such nonlinear impurity modes were considered, symmetric one- and two-hump modes and asymmetric one-hump mode. Their regions of existence and stability for both focusing and defocusing nonlinearity of a bulk medium and two different types of the impurity. An analytical stability criterion for nonlinear localized modes based on the results of the linear stability analysis of the generalized NLS equation was obtained.",

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AU - Kivshar, Yuri S.

AU - Bang, Ole

AU - Rasmussen, Jens J.

AU - Christiansen, Peter L.

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N2 - Spatially localized nonlinear modes supported by a pointlike impurity, in the framework of the generalized nonlinear Schrodinger (NLS) equation were analyzed. Three possible types of such nonlinear impurity modes were considered, symmetric one- and two-hump modes and asymmetric one-hump mode. Their regions of existence and stability for both focusing and defocusing nonlinearity of a bulk medium and two different types of the impurity. An analytical stability criterion for nonlinear localized modes based on the results of the linear stability analysis of the generalized NLS equation was obtained.

AB - Spatially localized nonlinear modes supported by a pointlike impurity, in the framework of the generalized nonlinear Schrodinger (NLS) equation were analyzed. Three possible types of such nonlinear impurity modes were considered, symmetric one- and two-hump modes and asymmetric one-hump mode. Their regions of existence and stability for both focusing and defocusing nonlinearity of a bulk medium and two different types of the impurity. An analytical stability criterion for nonlinear localized modes based on the results of the linear stability analysis of the generalized NLS equation was obtained.

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JF - Physical Review E

IS - 3 II

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Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

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