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

F. Kh Abdullaev*, A. Bouketir, A. Messikh, B. A. Umarov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)54-61
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume232
Issue number1
DOIs
StatePublished - 1 Aug 2007
Externally publishedYes

Bibliographical note

Funding Information:
F.K.A. is grateful to the Kulliyah of Science of IIUM (Malaysia) and the FAPESP (Brasil) for the partial financial support of his work. This research is partially funded by the SAGA Fund P77c of the Ministry of Science, Technology and Innovation (MOSTI) through the Academy of Sciences Malaysia(ASM).

Keywords

  • Discrete breather
  • Discrete nonlinear Schrödinger equation
  • Modulational instability
  • Stability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Modulational instability and discrete breathers in the discrete cubic-quintic nonlinear Schrödinger equation'. Together they form a unique fingerprint.

Cite this