  Under investigation in this work is the coupled Hirota system arising in
nonlinear fiber. The spectral analysis of the Lax pair is first carried out and
a Riemann-Hilbert problem is described. Then in the framework of the obtained
Riemann-Hilbert problem with the reflectionless case, N-soliton solution is
presented for the coupled Hirota system. Finally, via proper choices of the
involved parameters, a few plots are made to exhibit the localized structures
and dynamic characteristics of one-soliton solution.
