Initial-Boundary Value Problem for Two-Component Gerdjikov–Ivanov Equation with 3 × 3 Lax Pair on Half-Line

The Fokas unified method is used to analyze the initial-boundary value problem of two-component Gerdjikov–Ivanonv equation on the half-line. It is shown that the solution of the initial-boundary problem can be expressed in terms of the solution of a 3 × 3 Riemann–Hilbert problem. The Dirichlet to Neumann map is obtained through the global relation.