  The soliton resolution for the Harry Dym equation is established for initial
conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})$. Combining the
nonlinear steepest descent method and $\bar{\partial}$-derivatives condition,
we obtain that when $\frac{y}{t}<-\epsilon(\epsilon>0)$ the long time
asymptotic expansion of the solution $q(x,t)$ in any fixed cone
\begin{equation}
  C\left(y_{1}, y_{2}, v_{1}, v_{2}\right)=\left\{(y, t) \in R^{2} \mid
y=y_{0}+v t, y_{0} \in\left[y_{1}, y_{2}\right], v \in\left[v_{1},
v_{2}\right]\right\} \end{equation} up to an residual error of order
$\mathcal{O}(t^{-1})$. The expansion shows the long time asymptotic behavior
can be described as an $N(I)$-soliton on discrete spectrum whose parameters are
modulated by a sum of localized soliton-soliton interactions as one moves
through the cone and the second term coming from soliton-radiation
interactionson on continuous spectrum.
