Asymptotically-free solutions for the short-range nonlinear Schrodinger equation

We consider the nonlinear Schrodinger equation (NLS) with a power nonlinearity \u\(p-1)u, where 1 + 2/n < p. We show that for any free solution in L-2 or H-1 there exists a solution of NLS which approaches the free solution in the same space as t tends to infinity. We also show that the wave operators exist in <Sigma>(s) = H-s boolean AND F H-s for the critical power p = 1+ 4/(n + 2 s).