Preprint article · Journal article
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
Australian National University1
Department of Informatics and Mathematical Modeling, Technical University of Denmark2
Plasma Physics and Technology Programme, Risø National Laboratory for Sustainable Energy, Technical University of Denmark3
Risø National Laboratory for Sustainable Energy, Technical University of Denmark4
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.
Language: | English |
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Year: | 2001 |
Pages: | 036601 |
ISSN: | 10953787 , 1063651x , 24700053 , 24700045 , 15502376 and 15393755 |
Types: | Preprint article and Journal article |
DOI: | 10.1103/PhysRevE.63.036601 |
ORCIDs: | Bang, Ole , Juul Rasmussen, Jens and Christiansen, Peter Leth |
COLLAPSE INTERFACE LINEAR-CHAIN LOCALIZED MODES PHOTONIC CRYSTALS SCATTERING SCHRODINGER-EQUATION SOLITARY WAVES SOLITONS WAVE-GUIDE ARRAYS