Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honey

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We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.
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