Gap solitons in Bose-Einstein condensate loaded in a honeycomb optical lattice: nonlinear dynamical stability, tunneling, and self-trapping. (English) Zbl 1528.81154
Summary: We investigate the gap solitons of Bose-Einstein condensate in honeycomb optical lattices. It is found that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures be in-phase or out-of-phase. The nonlinear dynamical stabilities of these solitons are investigated using direct simulations of the Gross-Pitaevskii equation. For the unipole gap solitons, the nonlinear evolution shows dynamical stability or instability, which depends on the properties of atomic interactions and the dependence of soliton power. A fascinating property of dipole gap solitons is that they can present self-trapping or tunneling instabilities under atomic nonlinearity. The in-phase and out-of-phase of multipole gap solitons support different tunneling or self-trapping regimes. These results have an application to investigations of localized structures in nonlinear optics and Bose-Einstein condensate.
MSC:
| 81Q80 | Special quantum systems, such as solvable systems |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
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