A Vey theorem for nonlinear PDE

Sergei Kuksin; Galina Perelman

Séminaire Équations aux dérivées partielles (2009-2010)

  • Volume: 2009-2010, page 1-11

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Kuksin, Sergei, and Perelman, Galina. "A Vey theorem for nonlinear PDE." Séminaire Équations aux dérivées partielles 2009-2010 (2009-2010): 1-11. <http://eudml.org/doc/251169>.

@article{Kuksin2009-2010,
author = {Kuksin, Sergei, Perelman, Galina},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {A Vey theorem for nonlinear PDE},
url = {http://eudml.org/doc/251169},
volume = {2009-2010},
year = {2009-2010},
}

TY - JOUR
AU - Kuksin, Sergei
AU - Perelman, Galina
TI - A Vey theorem for nonlinear PDE
JO - Séminaire Équations aux dérivées partielles
PY - 2009-2010
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2009-2010
SP - 1
EP - 11
LA - eng
UR - http://eudml.org/doc/251169
ER -

References

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  1. D. Bambusi and B. Grébert, Birkhoff normal form for partial differential equations with tame modulus, Duke Math. J., 135 (2006), 507–567. Zbl1110.37057MR2272975
  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. Zbl0702.58024MR1036125
  4. H. Ito, Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv., 64 (1989), 412–461. Zbl0686.58021MR998858
  5. T. Kappeler, Fibration of the phase-space for the Korteweg-de Vries equation, Ann. Inst. Fourier, 41 (1991), 539–575. Zbl0731.58033MR1136595
  6. T. Kappeler and J. Pöschel, “KAM & KdV”, Springer, 2003. 
  7. S. Kuksin “Analysis of Hamiltonian PDEs”, Oxford University Press, Oxford, 2000. Zbl0960.35001MR1857574
  8. S. Kuksin, Damped-driven KdV and effective equation for long-time behaviour of its solutions, preprint (2009). MR2738999
  9. S. Kuksin and G.Perelman, Vey theorem in infinite dimensions and its application to KdV, Disc. Cont. Dyn. Syst. 27 (2010), 1-24. Zbl1193.37076MR2600759
  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. Zbl0632.35026MR878327
  11. J. Vey, Sur certain systèmes dynamiques séparables, Am. J. Math., 100 (1978), 591-614. Zbl0384.58012MR501141
  12. Nguyen T. Zung, Convergence versus integrability in Birkhoff normal form, Annals of Maths., 161 (2005), 141–156. Zbl1076.37045MR2150385

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