A Vey theorem for nonlinear PDE
Séminaire Équations aux dérivées partielles (Polytechnique) (2009-2010), Talk no. 18, 11 p.
@article{SEDP_2009-2010____A18_0,
author = {Kuksin, Sergei and Perelman, Galina},
title = {A Vey theorem for nonlinear PDE},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2009-2010},
note = {talk:18},
language = {en},
url = {http://www.numdam.org/item/SEDP_2009-2010____A18_0}
}

Kuksin, Sergei; Perelman, Galina. A Vey theorem for nonlinear PDE. Séminaire Équations aux dérivées partielles (Polytechnique) (2009-2010), Talk no. 18, 11 p. http://www.numdam.org/item/SEDP_2009-2010____A18_0/

[1] D. Bambusi and B. Grébert, Birkhoff normal form for partial differential equations with tame modulus, Duke Math. J., 135 (2006), 507–567. | MR 2272975 | Zbl 1110.37057

[2] L. H. Eliasson, “Hamiltonian systems with Poissson commuting integrals”, Ph.D Thesis, Stockholm University, 1984.

[3] L. H. Eliasson, Normal forms for Hamiltonian systems with Poisson commuting integrals—elliptic case, Comment. Math. Helv., 65 (1990), 4–35. | MR 1036125 | Zbl 0702.58024

[4] H. Ito, Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv., 64 (1989), 412–461. | MR 998858 | Zbl 0686.58021

[5] T. Kappeler, Fibration of the phase-space for the Korteweg-de Vries equation, Ann. Inst. Fourier, 41 (1991), 539–575. | Numdam | MR 1136595 | Zbl 0731.58033

[6] T. Kappeler and J. Pöschel, “KAM & KdV”, Springer, 2003.

[7] S. Kuksin “Analysis of Hamiltonian PDEs”, Oxford University Press, Oxford, 2000. | MR 1857574 | Zbl 0960.35001

[8] S. Kuksin, Damped-driven KdV and effective equation for long-time behaviour of its solutions, preprint (2009). | MR 2738999

[9] S. Kuksin and G.Perelman, Vey theorem in infinite dimensions and its application to KdV, Disc. Cont. Dyn. Syst. 27 (2010), 1-24. | MR 2600759 | Zbl 1193.37076

[10] N. Nikolenko, The method of Poincaré normal forms in problems of integrability of equations of evolution type, Russ. Math. Surveys, 41:5 (1986), 63–114. | MR 878327 | Zbl 0632.35026

[11] J. Vey, Sur certain systèmes dynamiques séparables, Am. J. Math., 100 (1978), 591-614. | MR 501141 | Zbl 0384.58012

[12] Nguyen T. Zung, Convergence versus integrability in Birkhoff normal form, Annals of Maths., 161 (2005), 141–156. | MR 2150385 | Zbl 1076.37045