Notion of profile at the blow-up for critical nonlinear Schrodinger equation

We will consider the L2 critical nonlinear Schrodinger equation in dimension smaller or equal to 4 in the full space. At the blow-up in the energy space, we have a concentration of a universal L2 mass and a strong limit outside. Again, in the rescaled version of the equation, a universal profile can be seen. Nethertheless, one can have different blow-up speed, and one can recover the information on the blow-up speed on the profile outside the singularity.