The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles

Sergei Grudsky, Christian Remling, Alexei Rybkin

We develop the inverse scattering transform for the KdV equation with real singular initial data $q(x)$ of the form $q(x)=r^{\prime }(x)+r(x{)}^2$, where $r\in L_{\text{loc}}^2$ and $r=…