Talk Abstracts

We provide an overview of recent developments in the study of small data modified scattering for the final state problem of the nonlinear Schrodinger equation (NLS) with long-range linear potentials. Given a prescribed asymptotic profile, we prove the existence of a global solution to NLS that scatters to the profile. This asymptotic profile is a combination of an Ozawa-type nonlinear modifier and a Yafaev-type linear modifier. It is constructed by solving a suitable reduced ODE and a Hamilton-Jacobi equation, respectively, associated with the nonlinearity and the long-range part of the linear potential. This talk is based on joint work with Masaki Kawamoto (Okayama University).