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Nonlinear localized waves in a periodic medium.

A A Sukhorukov¹, Y S Kivshar

¹Nonlinear Physics Group, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia.

Physical Review Letters

|August 11, 2001

Summary

We found stable nonlinear localized waves in a periodic medium with a nonlinear defect. Oscillatory wave instabilities linked to band-gap resonances were also identified.

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Area of Science:

Physics
Condensed Matter Physics
Nonlinear Dynamics

Background:

The Kronig-Penney model describes electron behavior in periodic potentials.
Nonlinear phenomena are crucial in understanding wave propagation in various media.
Localized states can exhibit unique properties in periodic systems.

Purpose of the Study:

To investigate the existence and stability of nonlinear localized waves.
To analyze these waves within the framework of the Kronig-Penney model with a nonlinear defect.
To identify novel types of stable localized states and associated instabilities.

Main Methods:

Mathematical analysis of nonlinear wave equations.
Application of the Kronig-Penney model with a nonlinear defect.
Stability analysis of localized solutions.

Main Results:

Demonstrated the existence of a novel type of stable nonlinear band-gap localized state.
Revealed a generic physical mechanism for oscillatory wave instabilities.
Linked these instabilities to band-gap resonances.

Conclusions:

Stable nonlinear localized states can exist in periodic media with nonlinear defects.
Band-gap resonances play a key role in wave instabilities.
The findings offer insights into nonlinear wave phenomena in structured materials.

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