Iasonas Hitzazis
(University of Patras, Dept. of Maths.)
Riemann-Hilbert Problems Associated to Boundary Value
Problems for the KdV Equation
We study Initial-Boundary Value Problems (IBVPs) for the KdV equation.
Emphasis is being given on the half-line problem, as well as on the interval
(two point) problem for the KdV equation. We apply the Inverse Scattering
method, based on the simultaneous spectral analysis of the two parts of the
associated Lax pair. The IBVPs under consideration are thereby formulated as
Riemann- Hilbert problems on the complex k-plane, where k is the spectral
parameter. We also discuss the analysis of the so-called global relation, by
means of which the unknown boundary values can be expressed in terms of the
known ones.