Hydrodynamic approach to constructing solutions of Hydrodynamic approach to constructing solutions of nonlinear Schrödinger equation in the critical case

Abstract

Proceeding from the hydrodynamic approach, we construct exact solutions to nonlinear Schrödinger 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."

11 pages. Proc.Amer.Math.Soc.(in press)