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.