Further scattering results for almost cubic nonlinear Schrِdinger equation

We present three results on the scattering of solutions for the almost cubic nonlinear Schrödinger 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.