Symmetry breaking, coupling management, and localized modes in dual-core discrete nonlinear-Schrödinger lattices |
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Authors: | H. SusantoP.G. Kevrekidis F.Kh. AbdullaevBoris A. Malomed |
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Affiliation: | a School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdomb Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515, USAc Physical-Technical Institute of the Academy of Sciences, 700084, Tashkent-84, G.Mavlyanov str., 2-b, Uzbekistand Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel |
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Abstract: | We introduce a system of two linearly coupled discrete nonlinear Schrödinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing type. We identify stability regions for fundamental onsite discrete symmetric solitons (single-site modes with equal norms in both components), as well as for two-site in-phase and twisted modes, the in-phase ones being completely unstable. The symmetry-breaking bifurcation, which destabilizes the fundamental symmetric solitons and gives rise to their asymmetric counterparts, is investigated too. It is demonstrated that the averaged equations provide a good approximation in all the cases. In particular, the symmetry-breaking bifurcation, which is of the pitchfork type in the framework of the averaged equations, corresponds to a Hopf bifurcation in terms of the original system. |
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Keywords: | Discrete nonlinear Schrö dinger equation Linear coupling Temporal management Discrete solitons Symmetry breaking |
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