  We consider the Cauchy problem for the classical Hirota equation on the line
with decaying initial data. Based on the spectral analysis of the Lax pair of
the Hirota equation, we first expressed the solution of the Cauchy problem in
terms of the solution of a Riemann-Hilbert problem. Further we apply nonlinear
steepest descent analysis to obtain the long-time asymptotics of the solution
in the critical transition region $|\frac{x}{t} -
\frac{\alpha^2}{3\beta}|t^{2/3} \leq M$, $M$ is a positive constant. Our result
shows that the long time asymptotics of the Hirota equation can be expressed in
terms of the solution of Painlev\'{e} $\mathrm{II}$ equation. Keywords: Hirota
equation, steepest descent method, Painlev\'{e} $\mathrm{II}$ equation,
long-time asymptotics.
