Nonlinear dynamical stability of gap solitons in Bose–Einstein condensate loaded in a deformed honeycomb optical lattice* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12065022, 12005173, 11747018, and 11565021), the Natural Science Foundation of Gansu Province of China (Grant No. 20JR10RA082), the China Postdoctoral Science Foundation (Grant No. 2020M680318), and the Scientific Research Foundation of NWNU

Abstract

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.