  This paper aims to present an application of Riemann-Hilbert approach to
treat higher-order nonlinear differential equation that is an eighth-order
nonlinear Schrodinger equation arising in an optical fiber. Starting from the
spectral analysis of the Lax pair, a Riemann-Hilbert problem is formulated.
Then by solving the obtained Riemann-Hilbert problem under the reflectionless
case, N-soliton solution is generated for the eighth-order nonlinear
Schrodinger equation. Finally, the three-dimensional plots and two-dimensional
curves with specific choices of the involved parameters are made to show the
localized structures and dynamic behaviors of one- and two-soliton solutions.
