We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|-1 in space dimension n≥2. We prove the existence of modified wave operators in the L2 sense on a dense set of small and sufficiently regular asymptotic states.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics