A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces

Communications in Mathematical Physics

Volumn 262, Issue 2, 2006, Pages 343-372

  Geng, Jiansheng ^a   You, Jiangong ^a  

^a NANJING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31144454113     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1497-0     Document Type: Article

References (20)

1. Bambusi, D.: Birkhoff normal form for some nonlinear PDEs. Commun. Math. Phys. 234, 253-285 (2003)
2. Bambusi, D., Berti, M.: A Birkhoff-Lewis type theorem for some Hamiltonian PDEs. SIAM J. Math. Anal. 37, 83-102 (2005)
3. Bourgain, J.: Quasiperiodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Ann. Math. 148, 363-439 (1998)
4. Bourgain, J.: Construction of periodic solutions of nonlinear wave equations in higher dimension. Geom. Funct. Anal. 5, 629-639 (1995)
5. Bourgain, J.: Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE., International Mathematics Research Notices, 1994, pp. 475-497
6. Bourgain, J.: Green's function estimates for lattice Schrödinger operators and applications, Annals of Mathematics Studies, 158. Princeton, NJ: Princeton University Press, 2005
7. Bourgain, J.: Nonlinear Schrödinger equations. Park City Series 5. Providence, RI: American Mathematical Society, 1999
8. Bourgain, J.: On diffusion in high-dimensional Hamiltonian systems and PDE. J. Anal. Math. 80, 1-35 (2000)
9. Craig, W., Wayne, C.E.: Newton's method and periodic solutions of nonlinear wave equations, Commun. Pure. Appl. Math. 46, 1409-1498 (1993)
10. Craig, W., Worfolk, P.: An integrable normal form for water waves in infinite depth. Physica D 84, 513-531 (1995)
11. Eliasson, L.H.: Perturbations of stable invariant tori for Hamiltonian systems. Ann. Sc. Norm. Sup. Pisa 15, 115-147 (1988)
12. Geng, J., You, J.: KAM tori of Hamiltonian perturbations of 1D linear beam equations. J.Math. Anal. Appl. 277, 104-121 (2003)
13. Geng, J., You, J.: A KAM Theorem for one dimensional Schrödinger equation with periodic boundary conditions. J. Diff. Eqs. 209, 1-56 (2005)
14. Kuksin, S.B.: Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum. Funct. Anal. Appl. 21, 192-205 (1987)
15. Kuksin, S.B.: Nearly integrable infinite dimensional Hamiltonian systems, Lecture Notes in Mathematics, 1556, Berlin: Springer, 1993
16. Kuksin, S.B., Pöschel, J.: Invariant Cantor manifolds of quasiperiodic oscillations for a nonlinear Schrödinger equation. Ann. Math. 143, 149-179 (1996)
17. Pöschel, J.: Quasi-periodic solutions for a nonlinear wave equation. Comment. Math. Helvetici 71, 269-296 (1996)
18. Pöschel, J.: A KAM theorem for some nonlinear partial differential equations. Ann. Sc. Norm. Sup. Pisa CI. Sci. 23, 119-148 (1996)
19. Pöschel, J.: On the construction of almost periodic solutions for a nonlinear Schrödinger equations. Erg. Th. Dynam. Syst. 22, 1537-1549 (2002)
20. Wayne, C.E.: Periodic and quasi-periodic solutions for nonlinear wave equations via KAM theory. Commun. Math. Phys. 127, 479-528 (1990)