Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations

Annals of Mathematics

Volumn 148, Issue 2, 1998, Pages 363-439

  Bourgain, J ^a,b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032272850     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121001     Document Type: Article

References (22)

1. J. BOURGAIN, Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, IMRN (1994), no. 11, 475-497.
2. _, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal. 5 (1995), 629-639.
3. _, Nonlinear Schrödinger equations, Park City Lectures, July 1995.
4. _, On Melnikov's persistency problem, Math. Res. Lett. 4 (1997), 445-458.
5. B. CONNES, Sur les coefficients des séries trigonométriques convergentes sphériquement, C. R. Acad. Sci. Paris 283 (1976), Sér. Aii, A159-A161.
6. W. CRAIG and C. E. WAYNE, Newton's method and periodic solutions of nonlinear wave equations, Comm. Pure Appl. Math. 46 (1993), 1409-1498.
7. W. CRAIG and C. E. WAYNE, Periodic solutions of nonlinear Schrödinger equations and the Nash-Moser method, Hamiltonian Mechanics, 103-122, NATO Adv. Sci. Inst. Ser. B Phys. 331 (1994), Plenum, NY.
8. L. H. ELIASSON, Perturbations of stable invariant tori for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa, CI. Sci. 15 (1988), 115-147.
9. J. FELDMAN, H. KNÖRRER, and E. TRUBOWITZ, Perturbatively unstable eigenvalues of a periodic Schrödinger operator, Comment. Math. Helv. 66 (1991), no. 4, 557-579.
10. J. FRÖHLICH, T. SPENCER, and P. WITTWER, Localization for a class of one-dimensional quasi-periodic Schrödinger operators, Comm. Math. Phys. 132 (1990), 5-25.
11. G. GALLAVOTTI, Invariant tori: a field-theoretic point of view of Eliasson's work, in Advances in Dynamical Systems and Quantum Physics, R. Figari, ed., World Scientific, 1995, 117-132.
12. E. GROSSWALD, Representations of Integers as Sums of Squares, Springer-Verlag, New York, 1985.
13. V. JARNICK, Über die Gitterpunkte auf konvexen Curven, Math. Z. 24 (1926), 500-518.
14. S. KUKSIN, Nearly integrable infinite-dimensional Hamiltonian systems LNM, 1556, Springer-Verlag, New York, 1993.
15. _, Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and its application to the Korteweg-de Vries equation, Mat. Sb. (NS), 136 (178) (1988), no. 3, 396-412, 431.
16. S. KUKSIN and J. PÖSCHEL, Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation, Annals of Math. 143 (1996), 149-179.
17. J. MOSER, On the theory of quasi-periodic motions, SIAM Review 8 (1966), 145-172.
18. _, Convergent series expansions for quasi-periodic motions, Math. Annalen 169 (1967), 136-176.
19. J. PÖSCHEL, On elliptic lower-dimensional tori in Hamiltonian systems, Math. Z. 202 (1989), 559-608.
20. _, On the Fröhlich-Spencer-estimate in the theory of Anderson localization, Manuscripta Math. 70 (1990) 27-37.
21. S. SURACE, The Schrödinger equation with a quasi-periodic potential, Trans AMS 1320, no. 1 (1990), 321-370.
22. C. E. WAYNE, Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Comm. Math. Phys. 127 (1990), 479-528.