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.