Near the blow-up time of the wave turbulence kinetic equation for the Schrödinger equation, the cumulants hierarchy cannot be approximated by the kinetic equation and must instead be replaced by a random field satisfying a nonlinear non-autonomous Schrödinger equation for all real times.
Pomeau, Asymptotic time behaviour of nonlinear classical field equations
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On the onset of correlations in Wave Turbulence close to singularities
Near the blow-up time of the wave turbulence kinetic equation for the Schrödinger equation, the cumulants hierarchy cannot be approximated by the kinetic equation and must instead be replaced by a random field satisfying a nonlinear non-autonomous Schrödinger equation for all real times.