On scattering for the quintic defocusing nonlinear Schr\"odinger   equation on \R \times \T^2
  We consider the problem of large data scattering for the quintic nonlinear Schr\"odinger equation on $\R \times \T^2$. 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. 
Zaher Hani and Benoit Pausader
math.AP