A KAM-theorem for some nonlinear partial differential equations

Jürgen Pöschel

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1996)

  • Volume: 23, Issue: 1, page 119-148
  • ISSN: 0391-173X

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Pöschel, Jürgen. "A KAM-theorem for some nonlinear partial differential equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 23.1 (1996): 119-148. <http://eudml.org/doc/84221>.

@article{Pöschel1996,
author = {Pöschel, Jürgen},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {persistence of invariant tori; infinite dimensional Hamiltonian; KAM-theorem},
language = {eng},
number = {1},
pages = {119-148},
publisher = {Scuola normale superiore},
title = {A KAM-theorem for some nonlinear partial differential equations},
url = {http://eudml.org/doc/84221},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Pöschel, Jürgen
TI - A KAM-theorem for some nonlinear partial differential equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1996
PB - Scuola normale superiore
VL - 23
IS - 1
SP - 119
EP - 148
LA - eng
KW - persistence of invariant tori; infinite dimensional Hamiltonian; KAM-theorem
UR - http://eudml.org/doc/84221
ER -

References

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  1. [1] A.I. Bobenko - S.B. Kuksin, The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation, Comment. Math. Helv.70 (1995), 63-112. Zbl0842.35099MR1314941
  2. [2] L.H. Eliasson, Perturbations of stable invariant tori for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci.15 (1988), 115-147. Zbl0685.58024MR1001032
  3. [3] S.B. Kuksin, Perturbation theory of conditionally periodic solutions of infinite dimensional Hamiltonian systems and its application to the Korteweg-de Vries equation, Mat. Sb.136 (1988); English transl. in Math. USSR-Sb.64 (1989), 397-413. Zbl0657.58033MR959490
  4. [4] S.B. Kuksin, Nearly integrable infinite-dimensional Hamiltonian systems, Lecture Notes in Mathematics1556, Springer, Berlin, 1993. Zbl0784.58028MR1290785
  5. [5] S.B. Kuksin - J. Pöschel, Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation, Ann. of Math. (to appear). Zbl0847.35130MR1370761
  6. [6] P.D. Lax, Developement of singularities of solutions of nonlinear hyperbolic partial differential equation, J. Math. Phys.5 (1964), 611-613. Zbl0135.15101MR165243
  7. [7] J. Pöschel, On elliptic lower dimensional tori in Hamiltonian systems, Math. Z.202 (1989), 559-608. Zbl0662.58037MR1022821
  8. [8] J. Pöschel, Quasi-periodic solutions for a nonlinear wave equation, Comment. Math. Helv. (to appear). Zbl0866.35013MR1396676
  9. [9] H. Rüssmann, On an inequality for trigonometric polynomials in several variables, Analysis, et cetera (P.H. Rabinowitz and E. Zehnder, eds.), Academic Press, Boston, pp. 545-562. Zbl0695.42003MR1039361
  10. [10] C.E. Wayne, Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Comm. Math. Phys.127 (1990), 479-528. Zbl0708.35087MR1040892

Citations in EuDML Documents

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  1. Dario Bambusi, Lyapunov center theorem for some nonlinear PDE's : a simple proof
  2. Benoît Grébert, Recent results on KAM for multidimensional PDEs
  3. Massimiliano Berti, Quasi-periodic solutions of PDEs
  4. Massimiliano Berti, Luca Biasco, Michela Procesi, KAM theory for the hamiltonian derivative wave equation
  5. Sandro Graffi, Méthodes KAM pour les opérateurs de Schrödinger non autonomes
  6. Massimiliano Berti, Soluzioni periodiche di PDEs Hamiltoniane
  7. Massimiliano Berti, Luca Biasco, Enrico Valdinoci, Periodic orbits close to elliptic tori and applications to the three-body problem
  8. Dario Bambusi, Alberto Maspero, Sistemi integrabili infinito dimensionali e loro perturbazioni

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