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We consider the nonlinear Schrodinger equation (NLS) with a power nonlinearity |u|p-1u , where 1 + 2/n < p. We show that for any free solution in L2 or H1 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 $\Sigma^s=H^s\cap{\cal F}H^s$ for the critical power p = 1+4/(n + 2s).

Asymptotically-Free Solutions for the Short-Range Nonlinear Schrödinger Equation