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Modulational instability and discrete breathers in the discrete cubic-quintic nonlinear Schrödinger equation. (English) Zbl 1125.37052

Summary: We investigate the properties of modulational instability and discrete breathers in the cubic-quintic discrete nonlinear Schrödinger equation. We analyze regions of modulational instabilities of nonlinear plane waves and derive 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.

MSC:

37K60 Lattice dynamics; integrable lattice equations
35Q55 NLS equations (nonlinear Schrödinger equations)
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
81V70 Many-body theory; quantum Hall effect
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