N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

For the case when all discrete spectral parameters are purely imaginary, an explicit N -soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions, consisting of arbitrary number of pure bright and/or dark solitons, is derived. Shifts of soliton positions due to collisions between solitons are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. Typical collisions between solitons are graphically shown.