Nonlinearity and disorder:  Classification and stability of nonlinear impurity modes

Andrey A. Sukhorukov, Yuri S. Kivshar, Ole Bang, Jens J. Rasmussen, and Peter L. Christiansen
Phys. Rev. E 63, 036601 – Published 14 February 2001
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Abstract

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.

  • Received 3 September 2000

DOI:https://doi.org/10.1103/PhysRevE.63.036601

©2001 American Physical Society

Authors & Affiliations

Andrey A. Sukhorukov1, Yuri S. Kivshar1, Ole Bang1,2, Jens J. Rasmussen3, and Peter L. Christiansen2

  • 1Optical Sciences Centre, Australian National University, Canberra ACT 0200, Australia
  • 2Department of Mathematical Modelling, Technical University of Denmark, Building 321, 2800 Kgs. Lyngby, Denmark
  • 3Risø National Laboratory, Optics and Fluid Dynamics Department, Risø, Roskilde DK-4000, Denmark

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Vol. 63, Iss. 3 — March 2001

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