Imperial College
Dept of Mathematics,
London SW7 2BZ, UK
b.pelloni@ic.ac.uk
Abstract
We illustrate a method of solving two-point boundary value problems for arbitrary linear evolution equations on the line, and its generalization to integrable nonlinear evolution equations, such as the famous Korteweg-deVries equation. This method is the extension of a general transform method recently introduced by Fokas to this particular class of problems, and it yields an explicit representation of the solution in a spectrally decomposed form. The new feature arising with two-point boundary value problems is the presence of a discrete spectrum in addition to the continuous spectrum associated with initial or boundary value problems on infinite or semi-infinite intervals.