Gap solitons in Bose-Einstein condensate loaded in a honeycomb optical lattice: Nonlinear dynamical stability, tunneling, and self-trapping

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. (C) 2021 Published by Elsevier B.V.

Automated summary

The study explores multipole gap solitons in honeycomb optical lattices, with bright solitary structures that can be in-phase or out-of-phase. Nonlinear dynamical stabilities of these solitons are investigated through direct simulations of the Gross-Pitaevskii equation, showing different stability or instability depending on the type of soliton and atomic interactions. Dipole gap solitons exhibit self-trapping or tunneling instabilities under atomic nonlinearity, supporting different regimes of tunneling or self-trapping for multipole solitons.