Further scattering results for almost cubic nonlinear Schrödinger equation

We present three results on the scattering of solutions for the almost cubic nonlinear Schrödinger equations. When initial datum has a small XpXp-norm, the solutions scatter in L2L2, when the initial datum is in HsHs with a small L2L2-norm with 0≤s≤10≤s≤1 then they scatter in HsHs. Finally, whenever we have global existence of H1H1 solutions, we also have scattering in the H0,1H0,1-norm.