Stabilised bright solitons in Bose—Einstein condensates in an expulsive parabolic and complex potential

The exact solitonic solutions of the one-dimensional nonlinear Schr?dinger equation, which describes the dynamics of bright soliton in Bose—Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially,when parameters satisfy the relation \lambda=2\gamma, the soliton is stable with time evolution without changing its shape and amplitude.