On the kinetic wave turbulence description for NLS. (English) Zbl 1431.35164
Summary: The purpose of this note is two-fold: A) We give a brief introduction into the problem of rigorously justifying the fundamental equations of wave turbulence theory (the theory of nonequilibrium statistical mechanics of nonlinear waves), and B), we describe a recent work of the authors in which they obtain the so-called wave kinetic equation, predicted in wave turbulence theory, for the nonlinear Schrödinger equation on short but nontrivial time scales.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K06 | General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
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