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We present how to control interactions between solitons, either bright ordark, in Bose-Einstein condensates by synchronizing Feshbach resonance andharmonic trap. Our results show that as long as the scattering length is to bemodulated in time via a changing magnetic field near the Feshbach resonance,and the harmonic trapping frequencies are also modulated in time, exactsolutions of the one-dimensional nonlinear Schr\"{o}dinger equation can befound in a general closed form, and interactions between two solitons aremodulated in detail in currently experimental conditions. We also proposeexperimental protocols to observe the phenomena such as fusion, fission, warp,oscillation, elastic collision in future experiments.

Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap