  The matrix-generalized Bogoliubov-de Gennes systems have recently been
considered by the present author [arXiv:1509.04242, Phys. Rev. B 93, 024512
(2016)], and time-dependent and self-consistent multi-soliton solutions have
been constructed based on the ansatz method. In this paper, restricting the
problem to the static case, we exhaustively determine the self-consistent
solutions using the inverse scattering theory. Solving the gap equation, we
rigorously prove that the self-consistent potential must be reflectionless. As
a supplementary topic, we elucidate the relation between the stationary
self-consistent potentials and the soliton solutions in the matrix nonlinear
Schr\"odinger equation. Asymptotic formulae of multi-soliton solutions for
sufficiently isolated solitons are also presented.
