Effect of Time-Dependent Atomic Scattering Length on Solitons in Bose-Einstein Condensates with a Complex Potential

We consider the one-dimensional nonlinear Schrödinger equationsthat describe the dynamics of a Bose--Einstein Condensates withtime-dependent scattering length in a complex potential. Our resultsshow that as long as the integrable relation is satisfied, exactsolutions of the one-dimensional nonlinear Schrödinger equationcan be found in a general closed form, and interactions between twosolitons are modulated in a complex potential. We find that thechanges of the scattering length and trapping potential can beeffectively used to control the interaction between two bright soliton.