Dynamics of the soliton-sound interaction in the quasi-one-dimensional Munoz-Mateo–Delgado equation

In this paper we study the effects of the transverse confinement strength on the dark solitons dynamics in quasi-one-dimensional Bose–Einstein condensates (BECs). The theoretical model is based on the Muoz-Mateo and Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since the MMD equation presents a nonpolynomial form, the soliton-sound recombination may not display the same pattern presented in the cubic model. We perform numerical simulations for harmonic and anharmonic (Gaussian) external potentials to compare both cases. All results via the MMD equation are in perfect agreement with the 3D simulations. Also, we noticed some differences between MMD and cubic models and changes in the soliton lifetime due to the values of the transverse confinement. (paper)