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Journées équations aux dérivées partiellesTable des matières de ce volume | Article précédent | Article suivantZaher Hani Out-of-equilibrium dynamics and statistics of dispersive PDE Journées équations aux dérivées partielles (2016), Exp. No. 5, 12 p., doi: 10.5802/jedp.646 Article PDF Mots clés: Modified scattering, nonlinear Schrödinger equation, wave guide manifolds, energy cascade, weak turbulence Résumé - Abstract The purpose of this note is to report on some recent advances in the study of out-of-equilibrium behavior of dispersive PDE. One can address this problematic from two different perspectives: a dynamical systems one, and a statistical physics one. The dynamical systems perspective corresponds to constructing solutions exhibiting “energy cascade” between scales, whereas the statistical physics perspective corresponds to deriving effective equations for the dynamics under some “macroscopic limits” in what is often called wave turbulence theory. 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