  Whether the Anderson localization can survive from the weak enough nonlinear
interaction is still an open question. In this Letter, we study the effect of
nonlinear interaction on disordered chain based on the wave turbulence theory.
It is found that the equipartition time $T_{eq}$ is inversely proportional to
the square of the nonlinearity strength $\lambda$, i.e.,
$T_{eq}\propto\lambda^{-2}$, in thermodynamic limit. This result has two
fundamentally important consequences. First, the Anderson localized modes can
not survive from arbitrarily weak nonlinearity. Secondly, contrary to popular
belief, disorder can lead to a more fast thermalization in the weak nonlinear
region, which is due to the emergence of three-wave resonance.
