Resonant averaging for weakly nonlinear stochastic Schrödinger equations

Sergei B. Kuksin[1]

  • [1] IMJ Universite Paris-Diderot (Paris 7) 5 rue Thomas Mann 75205 Paris Cedex 13

Séminaire Laurent Schwartz — EDP et applications (2013-2014)

  • Volume: 49, Issue: 4, page 1-9
  • ISSN: 2266-0607

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Kuksin, Sergei B.. "Resonant averaging for weakly nonlinear stochastic Schrödinger equations." Séminaire Laurent Schwartz — EDP et applications 49.4 (2013-2014): 1-9. <http://eudml.org/doc/275702>.

@article{Kuksin2013-2014,
affiliation = {IMJ Universite Paris-Diderot (Paris 7) 5 rue Thomas Mann 75205 Paris Cedex 13},
author = {Kuksin, Sergei B.},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {complex Ginzburg-Landau equation; small nonlinearity; limiting behaviour; stationary measure; averaging; effective equation},
language = {eng},
number = {4},
pages = {1-9},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Resonant averaging for weakly nonlinear stochastic Schrödinger equations},
url = {http://eudml.org/doc/275702},
volume = {49},
year = {2013-2014},
}

TY - JOUR
AU - Kuksin, Sergei B.
TI - Resonant averaging for weakly nonlinear stochastic Schrödinger equations
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2013-2014
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 49
IS - 4
SP - 1
EP - 9
LA - eng
KW - complex Ginzburg-Landau equation; small nonlinearity; limiting behaviour; stationary measure; averaging; effective equation
UR - http://eudml.org/doc/275702
ER -

References

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  1. J. Cardy, G. Falkovich, and K. Gawedzki, Non-equilibrium Statistical Mechanics and Turbulence, Cambridge University Press, Cambridge, 2008. MR2568424
  2. S. Kuksin and A. Maiocchi, Derivation of the Kolmogorov-Zakharov equation from the resonant-averaged stochastic NLS equation, http://arxiv.org/abs/1311.6794. Zbl1327.35462
  3. —, Resonant averaging for weakly nonlinear stochastic Schrödinger equations, http://arxiv.org/abs/1309.5022. 
  4. S. Kuksin and V. Nersesyan, Stochastic CGL equations without linear dispersion in any space dimension, Stoch PDE: Anal Comp 1 (2013), 389–423. Zbl1287.60093
  5. S. B. Kuksin and A. L. Piatnitski, Khasminskii - Whitham averaging for randomly perturbed KdV equation, J. Math. Pures Appl. 89 (2008), 400–428. Zbl1148.35077MR2401144
  6. S. B. Kuksin, Damped-driven KdV and effective equations for long-time behaviour of its solutions, GAFA 20 (2010), 1431–1463. Zbl1231.35205MR2738999
  7. —, Weakly nonlinear stochastic CGL equations, Ann. Inst. H. Poincaré - PR 49 (2013), 1033–1056. MR3127912
  8. S. Nazarenko, Wave Turbulence, Springer, Berlin, 2011. Zbl1220.76006MR3014432
  9. R. Peierls, On the kinetic theory of thermal conduction in crystals, Selected Scientific Papers of Sir Rudolf Peierls, with commentary, World Scientific, Singapore, 1997, pp. 15–48. 
  10. V. E. Zakharov and V. S. L’vov, Statistical description of nonlinear wave fields, Radiophys. Quan. Electronics 18 (1975), 1084–1097. MR462184
  11. V. Zakharov, V. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence, Springer, Berlin, 1992. Zbl0786.76002

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