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Modulational instability and discrete breathers in the discrete cubic-quintic nonlinear Schrödinger equation |
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| Authors: | F.Kh. Abdullaev A. Bouketir B.A. Umarov |
| Affiliation: | a Physical-Technical Institute, Uzbek Academy of Sciences, 700084, Tashkent-84, G. Mavlyanov str, 2-b, Uzbekistan b Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P.O. Box 10, 50728 Kuala Lumpur, Malaysia c Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 10, 50728 Kuala Lumpur, Malaysia |
| 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. |
| Keywords: | Modulational instability Discrete breather Discrete nonlinear Schrö dinger equation Stability |
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