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Soliton on the semi-infinite band gap of BEC in an optical lattice. (English) Zbl 1217.82011

Summary: By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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