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In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution{   q  1   (  x  ,  t  )  ,   q  2   (  x  ,  t  )  }   $\{q_1(x,t),q_2(x,t)\}$    exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameterλ   $\lambda$   .

Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrödinger Equations on the Half-line