Dynamics of matter-wave solitons in Bose-Einstein condensates with time-dependent scattering length and complex potentials

Abstract

We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D) Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) with time-dependent scattering length in varying trapping potentials with feeding/loss term. By performing a modified lens-type transformation, we reduce the GP equation into a classical nonlinear Schrodinger (NLS) equation with distributed coefficients and find its integrable condition. Under the integrable condition, we apply the generalized Jacobian elliptic function method (GJEFM) and present exact analytical solutions which describe the propagation of a bright and dark solitons in BECs. Their stability is examined using analytic method. The obtained exact solutions show that the amplitude of bright and dark solitons depends on the scattering length, while their motion and the total number of BEC atoms depend on the external trapping potential. Our results also shown that the loss of atoms can dominate the aggregation of atoms by the attractive interaction, and thus the peak density can decrease in time despite that the strength of the attractive interaction is increased.