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 language | English |
|---|---|
| Pages (from-to) | 54-61 |
| Number of pages | 8 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 232 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Aug 2007 |
| Externally published | Yes |
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