The Neumann and Robin problems for the Korteweg-de Vries equation on the half-line

The well-posedness of the Neumann and Robin problems for the Korteweg-de Vries equation is studied with data in Sobolev spaces. Using the Fokas unified transform method, the corresponding linear problems with forcing are solved and solution estimates are derived. Then, using these, an iteration map is defined, and it is proved to be a contraction in appropriate solution spaces after the needed bilinear estimates are derived.