On a kinetic equation in weak turbulence theory for the nonlinear   Schr\"odinger equation
  The results from J. Stat. Phys. 159:668-712 & 163:1350-1393, on a quadratic kinetic equation in the analysis of the long time asymptotics of weak turbulence theory for the nonlinear Schr\"odinger equation, are summarized and placed in context. Additionally, two conjectures on self-similar solutions are presented, and backed with consistency analysis and numerics. 
A.H.M. Kierkels
math-ph math.MP