Abstract
We relate the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions to that of the matrix Schrödinger equation. This (shifted) Miura transformation converts the focusing matrix nonlinear Schrödinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method of solving the Marchenko integral equations by separation of variables to derive the multisoliton solutions of this nonlocal equation, thus proposing a method to solve the reflectionless matrix NLS equation.
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