We consider the averaged dispersion-managed (DM) fiber system equation, which governs the dynamics of the core of the DM solitons. For a special case of such a system equation, we derive the exact soliton solutions using the Darboux transformation. Further, we discuss the interaction scenario between two neighboring solitons. Finally, we derive a dark soliton solution for such a system by assuming an ansatz, and the interaction between neighboring dark solitons is discussed.