Further scattering results for almost cubic nonlinear Schrodinger equation

We present three results on the scattering of solutions for the almost cubic nonlinear Schrodinger equations. When initial datum has a small X-p-norm, the solutions scatter in L-2, when the initial datum is in H-s with a small L-2-norm with 0 <= s <= 1 then they scatter in H-s. Finally, whenever we have global existence of H-1 solutions, we also have scattering in the H-0.1-norm. (C) 2010 Elsevier Ltd. All rights reserved.