  We develop the inverse scattering transform for the KdV equation with real
singular initial data $q(x)$ of the form $q(x) = r'(x) + r(x)^2$, where $r\in
L^2_{\textrm{loc}}$ and $r=0$ on $\mathbb R_+$. As a consequence we show that
the solution $q(x,t)$ is a meromorphic function with no real poles for any
$t>0$.
