Integrable Systems seminar: Soliton solutions for the nonlinear Schroedinger equation on the half-line

Kevin Gruner (University of Cologne) will present his research in Integrable Systems.

The Inverse Scattering Method (ISM) was first introduced by Gardner, Greene, Kruskal and Miura in 1967. The ISM represents a nonlinear version of the Fourier transform and is applied to several initial value problems on the full line. Further, various types of soliton solutions can be obtained by means of the ISM. Later on, PDEs on the half-line with an initial and a boundary condition has been investigated and this lead to the modification of the ISM into what is now known as the Unified Transform (or the Fokas method).

Kevin Gruner will present the idea of the ISM and a recent method involving Darboux transformations to construct soliton solutions for integrable initial-boundary value problems in the model of the nonlinear Schroedinger equation on the half-line.

For further information, please contact Professor Allan P Fordy.