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Nonlinearity and disorder: classification and stability of nonlinear impurity modes
A A Sukhorukov1, Y S Kivshar, O Bang
1Optical Sciences Centre, Australian National University, Canberra ACT 0200, Australia.
Summary
We investigated energy localization in nonlinear systems with impurities. We identified different localized modes and their stability, revealing dynamics like decay, switching, and collapse.
Area of Science:
- Nonlinear physics
- Condensed matter theory
- Mathematical physics
Background:
- Inhomogeneous nonlinear systems exhibit complex energy localization phenomena.
- Nonlinear impurities can significantly alter the behavior of these systems.
- Understanding localized modes is crucial for controlling energy flow.
Purpose of the Study:
- To analyze the competition between physical mechanisms of energy localization.
- To investigate nonlinear impurity modes in the generalized nonlinear Schrödinger equation.
- To determine the stability and dynamics of these localized modes.
Main Methods:
- Analysis of spatially localized modes supported by a nonlinear impurity.
- Description of one- and two-hump symmetric and asymmetric localized modes.
- Derivation of an analytical stability criterion for nonlinear localized modes.
Main Results:
- Identified three types of nonlinear impurity modes: symmetric (one- and two-hump) and asymmetric.
- Characterized modes for focusing/defocusing nonlinearity and attractive/repulsive impurities.
- Detailed analysis of power-law nonlinearity and instability-induced dynamics.
Conclusions:
- The study provides a comprehensive understanding of nonlinear impurity modes.
- Stability criteria and dynamic behaviors like decay, switching, and collapse were elucidated.
- Findings are relevant for controlling energy localization in engineered nonlinear systems.