THE INITIAL-BOUNDARY VALUE FOR THE COMBINED SCHRODINGER AND GERDJIKOV-IVANOV EQUATION ON THE HALF-LINE VIA THE RIEMANN-HILBERT APPROACH

摘要

The Fokas method is used to study the initial-boundary value problem for the combined Schrodinger 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.. The jump matrices are given on the basis of the spectral functions, which are not independent, but are related by a global relation.