Abstract
Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schrödinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel’fand-Levitan-Marchenko [Amer. Math. Soc. Transl. 1, 253 (1955)] equation.
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