The initial-boundary value for the combined Schrödinger and Gerdjikov–Ivanov equation on the half-line via the Riemann–Hilbert approach

The Fokas method is used to study the initial-boundary value problem for the combined Schrödinger and Gerdjikov–Ivanov equation on the half-line. Assuming that the solution $u(x,t)$ exists, it can be represented by the unique solution of a matrix Riemann–Hilbert problem formulated on the plane of the complex spectral parameter $\xi$. The jump matrices are given on the basis of the spectral functions, which are not independent, but are related by a global relation.