Exact solitons in the Gross-Pitaevskii equation with time-modulated nonlinearity

Exact solitonic solutions of the Gross-Pitaevskii equation with time-modulated nonlinearity of a(t) = a(0) / (t + t(0)) are obtained. With help of these solutions, we analyze the properties of Feshbach-managed solitons in Bose-Einstein condensates in details. Our results show that the parameters of atomic matter waves can be manipulated by proper variation of the scattering length. In particular, an exact two-solition solution is given, from which, it is shown that the separation between the neighboring solitons can be effectively maintained by allowing the solitons to have unequal initial amplitudes.