The initial-boundary value problem for the Korteweg-de Vries equation
  We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on the right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators, extending the techniques of Colliander-Kenig (2002). 
Justin Holmer