Modulating the amplitude of dark soliton by scattering-length management in Bose-Einstein condensates

We present a family of soliton solutions of the quasi-one-dimensional Bose-Einstein condensates with time-dependent scattering length, by developing multiple-scale method combined with truncated Painlevé expansion. Then, by numerical calculating the solutions, it is shown that there exhibit two types of dark solitons—black soliton (the zero minimum amplitude at its center) and gray soliton (the minimum density does not drop to zero) in a repulsive condensate. Furthermore, we propose experimental protocols to realize the exchange between black and gray solitons by varying the scattering length via the Feshbach resonance in currently experimental conditions.