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We relate the scattering theory of the focusing AKNS system with vanishingboundary conditions to that of the matrix Schroedinger equation. Thecorresponding Miura transformation which allows this connection, converts thefocusing matrix nonlinear Schroedinger (NLS) equation into a new nonlocalintegrable equation. We apply the matrix triplet method to derive themultisoliton solutions of the nonlocal integrable equation, thus proposing anew method to solve the matrix NLS equation.

From the AKNS system to the matrix Schroedinger equation with vanishing potentials: Direct and inverse problems