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This article is cited in 5 scientific papers (total in 5 papers)
MATHEMATICS
On the Zakharov–Lvov stochastic model for wave turbulence
A. V. Dymova, S. B. Kuksinbcd a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Université Paris VII – Denis Diderot
c Shandong University, Jinan, PRC
d Saint Petersburg State University
Abstract:
In this paper we discuss a number of rigorous results in the stochastic model for wave turbulence due to Zakharov–L'vov. Namely, we consider the damped/driven (modified) cubic nonlinear Schrödinger equation on a large torus and decompose its solutions to formal series in the amplitude. We show that when the amplitude goes to zero and the torus’ size goes to infinity the energy spectrum of the quadratic truncation of this series converges to a solution of the damped/driven wave kinetic equation. Next we discuss higher order truncations of the series.
Keywords:
wave turbulence, energy spectrum, wave kinetic equation, kinetic limit, nonlinear Schrödinger equation, stochastic perturbation.
Citation:
A. V. Dymov, S. B. Kuksin, “On the Zakharov–Lvov stochastic model for wave turbulence”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 29–37; Dokl. Math., 101:2 (2020), 102–109
Linking options:
https://www.mathnet.ru/eng/danma4 https://www.mathnet.ru/eng/danma/v491/p29
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