On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T²

Abstract

We consider the problem of large‐data scattering for the quintic nonlinear Schrödinger equation on R × T 2 . This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a “large‐scale profile”) that controls the asymptotic behavior of the solutions. © 2014 Wiley Periodicals, Inc.