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The Marchenko method is presented for the linear system associated with the derivative NLS (nonlinear Schrödinger) system. The system of linear Marchenko integral equations is derived in order to solve the corresponding inverse scattering problem. Through the use of the inverse scattering transform, solutions are obtained for the derivative NLS system. Explicit solution formulas are developed in closed form by using as input a pair of matrix triplets corresponding to reflectionless scattering data.

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