  In this paper, we obtain the long-time asymptotics of complex mKdV equation
via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem
of complex mKdV equation is transformed into the corresponding Riemann-Hilbert
problem on the basis of the Lax pair and the scattering matrix. After that
Riemann-Hilbert problems are converted through a decomposition of the
matrix-valued spectral function and factorizations of the jump matrix for
Riemann-Hilbert problem. Finally, by solving the last model problem, the
long-time asymptotics of complex mKdV equation are derived.
