Modulational instability and discrete breathers in the discrete cubic–quintic nonlinear Schrödinger equation

We investigate the properties of modulational instability and discrete breathers in the cubic–quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. Using the Page approach [J.B. Page, Phys. Rev. B 41 (1990) 7835], we derive th...

Full description

Saved in:
Bibliographic Details
Published in:Physica. D 2007-08, Vol.232 (1), p.54-61
Main Authors: Abdullaev, F.Kh, Bouketir, A., Messikh, A., Umarov, B.A.
Format: Article
Language:English
Subjects:
Discrete breather
Discrete nonlinear Schrödinger equation
Exact sciences and technology
Modulational instability
Physics
Stability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate the properties of modulational instability and discrete breathers in the cubic–quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. Using the Page approach [J.B. Page, Phys. Rev. B 41 (1990) 7835], we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The application to the existence of localized modes in the Bose–Einstein condensate (BEC) with three-body interactions in an optical lattice is discussed. The numerical simulations agree with the analytical predictions.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2007.05.005