Dynamical instability of dark solitons perturbed by an optical lattice in the quasi-one-dimensional Muñoz-Mateo–Delgado equation

We study the dynamical instability of a dark soliton perturbed by an optical lattice (OL) in a quasi-one-dimensional Bose–Einstein condensate (BEC). The system is described by the Muñoz-Mateo–Delgado (MMD) equation, which is an effective one-dimensional model for the axial dynamics of a cigar-shaped BEC with repulsive interatomic interactions, accurately accounting for the contribution from the transverse structure. During the unstable propagation of moving dark solitons, sound waves are emitted. The results obtained from the MMD equation differ from those of the standard cubic model. We perform numerical simulations to analyze the influence of the optical lattice combined with harmonic confinement on the soliton lifetime. In this configuration, we observe that increasing the depth of the OL leads to a reduction in the lifetime of localized solutions.