LAUSR

Abstract The dynamical stability properties of gap solitons in a quasi-one-dimensional Bose–Einstein Condensate (BEC) loaded in a Jacobian elliptic sine potential are investigated numerically. The Gross–Pitaevskii equation (GPE) is adopted to describe the dynamical behaviors for such a system under the mean-field approximation. Firstly, we presented the band-gap structures via linearizing the GPE. Secondly, the gap solitons are gotten by the Newton-Conjugate-Gradient (NCG) method. Thirdly, the linear stability analysis and nonlinear dynamical evolution method are used to investigate the dynamical stability properties of gap solitons given by the NCG method. It is found that there exist both stable gap solitons and unstable gap solitons with rich structures in such a nonlinear system. The modulus of external potential has distinctly influence on the instability property of the gap solitons.