Formal Expansions in Stochastic Model for Wave Turbulence 2: Method of Diagram Decomposition

被引：0
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作者：
Andrey Dymov
Sergei Kuksin
机构：
[1] Steklov Mathematical Institute of RAS,
[2] National Research University Higher School of Economics,undefined
[3] Skolkovo Institute of Science and Technology,undefined
[4] Institut de Mathémathiques de Jussieu–Paris Rive Gauche,undefined
[5] CNRS,undefined
[6] Université Paris Diderot,undefined
[7] UMR 7586,undefined
[8] Peoples’ Friendship University of Russia (RUDN University),undefined
来源：
Journal of Statistical Physics | 2023年 / 190卷
关键词：
Wave turbulence; Weak turbulence; Wave kinetic equation; Wave kinetic limit; Feynman diagrams; Diagram decomposition; Fast oscillating integrals; Nonlinear Schrödinger equation;
D O I：
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学科分类号：
摘要：
In this paper we continue to study small amplitude solutions of the damped cubic NLS equation, driven by a random force [the study was initiated in our previous work Dymov and Kuksin (Commun Math Phys 382:951–1014, 2021) and continued in Dymov et al. (The large-period limit for equations of discrete turbulence 2021, arXiv:2104.11967)]. We write solutions of the equation as formal series in the amplitude and discuss the behaviour of this series under the wave turbulence limit, when the amplitude goes to zero, while the space-period goes to infinity.
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