Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential

Communications in Mathematical Physics

Volumn 204, Issue 1, 1999, Pages 207-247

  Bourgain, J ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033247272     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050644     Document Type: Article

References (9)

1. [B1] Bourgain, J.: On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. IMRN N6, 277-304 (1996)
2. [B2] Bourgain, J.: Construction of Quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. IMRN N11, 475-497 (1994)
3. [B3] Bourgain, J.: Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Annals of Math. 148, 2, 363-439 (1998)
4. [B4] Bourgain, J.: Construction of periodic solutions of nonlinear wave equations in higher dimension. GAFA 4, 629-639 (1995)
5. [C-W] Craig, W., Wayne, W.: Newton's method and periodic solutions of nonlinear wave equations. CPAM 46, 1409-1501 (1993)
6. [Ku] Kuksin, S.: Infinite dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE. CMP 167, 531-552 (1995)
7. [F-S-W] Fröhlich, J., Spencer, T., Wittwer, R.: Localization for a class of one dimensional quasi-periodic Schrödinger operators. CMP 132, N1, 5-25 (1990)
8. [S] Spencer, T.: Private communications
9. [St] Staffilani, G.: Quadratic forms for a 2D semilinear Schrödinger equation. Duke Math. J. 86, N1, 79-108 (1997)