Riemann–Hilbert approach to the higher-order Kaup-Newell equation on the half line

The higher-order Kaup–Newell equation is examined by applying the Fokas unified method on the half-line. We demonstrate that the solution can be expressed in relation to the resolution of the Riemann–Hilbert problem. The jump matrix for this problem is derived from the spectral matrix, which is calculated based on both the initial conditions and the boundary conditions. The jump matrix is explicitly dependent and expressed through the spectral functions, which are derived from the initial and boundary information, respectively. These spectral functions are interdependent and adhere to a so-called global relationship.