Scattering and spectral theory for Stark Hamiltonians in one dimension.
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
Structured matrix numerical solution of the nonlinear Schrödinger equation by the inverse scattering transform.