  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.
