Abstract :
Consider the NLS with periodic boundary conditions in 1D
iut + u + Mu ± εu|u|4 = 0, (0.1)
where M is a random Fourier multiplier defined by
Mu(n) = Vn ˆu(n) (0.2)
and (Vn)n∈Z are independently chosen in [−1, 1].
The quintic nonlinearity in (0.1) is unimportant and may be replaced by u|u|p−2, p ∈ 2Z, p 4.
We give a proof of the following fact.
