Riemann–Hilbert method for multi-soliton solutions of a fifth-order nonlinear Schrödinger equation

Abstract

A fifth-order nonlinear Schrodinger equation which describes the one-dimensional anisotropic Heisenberg ferromagnetic spin chain is under investigation in this paper. Starting from the spectral analysis, a matrix Riemann–Hilbert problem is established on the real axis. Then, through solving the resulting matrix Riemann–Hilbert problem under the condition of no reflection, we systematically derive multi-soliton solutions to the fifth-order nonlinear Schrodinger equation. In addition, the localized structures of one-soliton solution are shown vividly via a few plots.