Two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions

An explicit two-soliton solution for the derivative nonlinear Schr"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons.