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

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. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Authors
Dymov A. , Kuksin S.
Journal
Journal of Statistical Physics
Publisher
Springer New York LLC
Issue number
1
Language
English
State
Published
Link
External link
DOI
10.1007/S10955-022-02998-0
Number
3
Volume
190
Year
2023
Organizations
  • 1 Steklov Mathematical Institute of RAS, Moscow, 119991, Russian Federation
  • 2 National Research University Higher School of Economics, Moscow, 119048, Russian Federation
  • 3 Skolkovo Institute of Science and Technology, Skolkovo, 143005, Russian Federation
  • 4 Institut de Mathémathiques de Jussieu–Paris Rive Gauche, CNRS, Université Paris Diderot, UMR 7586, Sorbonne Paris Cité, Paris, 75013, France
  • 5 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Diagram decomposition; Fast oscillating integrals; Feynman diagrams; Nonlinear Schrödinger equation; Wave kinetic equation; Wave kinetic limit; Wave turbulence; Weak turbulence
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