A new approach to Scattering: On the Asymptotic states of Nonlinear Dispersive and Hyperbolic equations with General Data

I will present a new approach to finding the asymptotic states of Nonlinear Wave Equations with general initial data.
In particular, we show for a large class of equations, that all asymptotic states are linear combinations of free wave, localized parts (solitons, breathers..) and a possibility of self-similar solutions as well in some cases. These results hold for initial data for which the H^1 Sobolev norm (the energy norm) is uniformly bounded in time.
This answers the question of Asymptotic Completeness to a large class of equations, including for the first time, equations with time dependent potentials.
These are joint works with Baoping Liu (Peking Univ) and Xiaoxu Wu (Rutgers).