In this paper we consider the nonlinear Schrodinger (XLS) equation in the repulsive case and without any renormalization linear term in it. The Backlund transformation (BT) of s single-kink soliton is integrated explicitly yielding the doublc-kink-soliton solution of the NLS equation. By a recursive application of the nonlinear superposition principle for the NLS equation we obtain the multiple-kink-soliton solution. The soliton shifts due to mutual interactions are calculated and it is shown that only paired collisions occur.