Riemann-Hilbert problem for a fourth-order dispersive nonlinear Schrödinger equation on the half-line

Abstract

In this paper, we investigate a fourth-order dispersive nonlinear Schrödinger equation on the half-line, which has the physical applications in Heisenberg ferromagnetic spin. Solutions for this equation are expressed in form of the unique solution for Riemann-Hilbert problem on the complex k-plane. The related jump matrices are explicitly defined by the initial and boundary values, which are located in the Schwartz space. The global relation about the spectral functions is established.