  In this paper, we study the long time asymptotic behavior for the initial
value problem of the modified Camassa-Holm (mCH) equation in the solitonic
region \begin{align}
  &m_{t}+\left(m\left(u^{2}-u_{x}^{2}\right)\right)_{x}+\kappa u_{x}=0, \quad
m=u-u_{x x}, \nonumber
  &u(x, 0)=u_{0}(x),\nonumber \end{align} where $\kappa$ is a positive
constant. Based on the spectral analysis of the Lax pair associated with the
mCH equation and scattering matrix, the solution of the Cauchy problem is
characterized via the solution of a Riemann-Hilbert (RH) problem. Further using
the $\overline\partial$ generalization of Deift-Zhou steepest descent method,
we derive different long time asymptotic expansion of the solution $u(x,t)$ in
different space-time solitonic region of $x/t$. These asymptotic approximations
can be characterized with an $N(\Lambda)$-soliton whose parameters are
modulated by a sum of localized soliton-soliton interactions as one moves
through the region with diverse residual error order from $\overline\partial$
equation: $\mathcal{O}(|t|^{-1+2\rho})$ for
$\xi=\frac{y}{t}\in(-\infty,-0.25)\cup(2,+\infty)$ and
$\mathcal{O}(|t|^{-3/4})$ for $\xi=\frac{y}{t}\in(-0.25,2)$. Our results also
confirm the soliton resolution conjecture and asymptotically stability of
N-soliton solutions for the mCH equation.
