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Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schrödinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N -soliton solutions on the half-line. Using dressing transformations combined with a mirror image technique, factorization of soliton-soliton and soliton-boundary interactions is proved. We discover a new object, which we call reection map, that satises a set-theoretical reectiondoi:10.1088/0951-7715/27/6/1081 fatcat:z5llnj6rsvhzlc2gytht5nv7hi