Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4640135 | Journal of Computational and Applied Mathematics | 2011 | 6 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
H. Susanto, P.G. Kevrekidis, F.Kh. Abdullaev, Boris A. Malomed,