A Vey theorem for nonlinear PDE
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé 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) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:18},
     pages = {1--11},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2009-2010},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2009-2010____A18_0/}
}
TY  - JOUR
AU  - Kuksin, Sergei
AU  - Perelman, Galina
TI  - A Vey theorem for nonlinear PDE
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:18
PY  - 2009-2010
SP  - 1
EP  - 11
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2009-2010____A18_0/
LA  - en
ID  - SEDP_2009-2010____A18_0
ER  - 
%0 Journal Article
%A Kuksin, Sergei
%A Perelman, Galina
%T A Vey theorem for nonlinear PDE
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:18
%D 2009-2010
%P 1-11
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2009-2010____A18_0/
%G en
%F SEDP_2009-2010____A18_0
Kuksin, Sergei; Perelman, Galina. A Vey theorem for nonlinear PDE. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé 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 | Zbl

[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 | Zbl

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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

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