Abstract
We present a simple but powerful method for constructing multisoliton complexes of the coupled nonlinear Schrödinger equation. Our method is based on the Bäckrund-Darboux transformation. A closed form of the matrix determinant is given for multisoliton complexes, including the case of a nonvanishing background. We explicitly work out the solutions of two-, three-, and four-component coupled nonlinear Schrödinger equations.
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