  We relate the scattering theory of the focusing AKNS system with vanishing
boundary conditions to that of the matrix Schroedinger equation. The
corresponding Miura transformation which allows this connection, converts the
focusing matrix nonlinear Schroedinger (NLS) equation into a new nonlocal
integrable equation. We apply the matrix triplet method to derive the
multisoliton solutions of the nonlocal integrable equation, thus proposing a
new method to solve the matrix NLS equation.
