“…In addition, to tackle the long standing open conjecture about the long time behavior of high Sobolev norms H s ps ą 1q of solutions of dispersive equations on the torus, discussed in the works of Bourgain [1] and Colliander, Staffilani, Keel, Takaoka, Tao [8], the rigorous justification of wave turbulence theory has been revisited during the last few years in [2,6,7,9,10,15,16,17,18,19,20,22,26,27,48].…”