Factorization of the scattering matrix and the location of the eigenvalues of the Manakov–Zakharov–Shabat system

We show the scattering matrix associated to the Manakov–Zakharov–Shabat (MZS) system can be factorized as the product of two scattering matrices associated to the Zakharov–Shabat (ZS) system of the Nonlinear Schrödinger (NLS) equation, whenever the initial conditions of the Manakov system have disjoint support. Moreover, if these initial conditions are assumed to be single-lobe, the eigenvalues of the MZS system are purely imaginary.