Hydrodynamic approach to constructing solutions of Hydrodynamic approach   to constructing solutions of nonlinear Schr\"odinger equation in the critical   case
  Proceeding from the hydrodynamic approach, we construct exact solutions to nonlinear Schr\"odinger equation with special properties. The solutions describe collapse, in finite time, and scattering, over infinite time, of wave packets. They generalize known blow-up solutions based on the "ground state." 
Olga S. Rozanova