Dynamics of matter-wave solitons in Bose-Einstein condensates with time-dependent scattering length and complex potentials
Tóm tắt
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 Schrödinger (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.
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