Data di Pubblicazione:
2015
Citazione:
Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation / S. Kuksin, A. Maiocchi. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 309(2015 Aug 01), pp. 31621.65-31621.70. [10.1016/j.physd.2015.04.002]
Abstract:
We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kinetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analysed with full rigour in Kuksin and Maiocchi (0000), and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the Kolmogorov-Zakharov spectra.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Kolmogorov-Zakharov spectra; Wave kinetic equation; Weak turbulence; Condensed Matter Physics; Statistical and Nonlinear Physics
Elenco autori:
S. Kuksin, A. Maiocchi
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