  In this paper, we mainly analyze the long-time asymptotics of high-order
soliton for the Hirota equation. Two different Riemann-Hilbert representations
of Darboux matrix with high-order soliton are given to establish the
relationships between inverse scattering method and Darboux transformation. The
asymptotic analysis with single spectral parameter is derived through the
formulas of determinant directly. Furthermore, the long-time asymptotics with
$k$ spectral parameters is given by combining the iterated Darboux matrix and
the result of high-order soliton with single spectral parameter, which
discloses the structure of high-order soliton clearly and is possible to be
utilized in the optic experiments.
