The GLM representation of the two-component nonlinear Schrödinger equation on the half-line

The Gelfand-Levitan-Marchenko representation is used to analyze the initialboundary value problem of two-component nonlinear Schr¨odinger equation on the half-line.It has shown that the global relation can be effectively analyzed by the Gelfand-LevitanMarchenko representation. we also derive expressions for the Dirichlet-to-Neumann map to characterize the unknown boundary values.