Abstract

We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.

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