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Soliton Solutions in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

We present both the bright and dark solitons of Bose–Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a(t) = g0exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].