Singular Miura type initial profiles for the KdV equation
  We show that the KdV flow evolves any real singular initial profile q of the form q=r'+r^2, where r\inL_{loc}^2, r|_{R_+}=0 into a meromorphic function with no real poles. 
Sergei Grudsky and Alexei Rybkin
nlin.SI math.AP math.SP