250127 VO Introduction to inverse scattering theory with applications (2008W)

The main objective of the course is to get acquainted with the inverse scattering transform. We will first examine in detail two classical inverse scattering problems on the half-axis and on the whole axis. We solve them for the case of Jacobi operators, where these methods can be
demonstrated most transparently. Then we will study the application of the Lax pair formalism and the inverse scattering transform method for the solution of the corresponding initial value problem of the Toda lattice
(in the whole axis case). We will also draw analogies with similar problems for one-dimensional Schrödinger operators and the initial value problems of the Korteveg- de Vries equation.