%0 Journal Article
%T The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles
%A Sergei Grudsky
%A Christian Remling
%A Alexei Rybkin
%J Mathematics
%D 2014
%I arXiv
%R 10.1063/1.4930001
%X 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 $t>0$.
%U http://arxiv.org/abs/1412.2184v1