On nonlinear Schrödinger equations

Jean Bourgain

Publications Mathématiques de l'IHÉS (1998)

  • Volume: S88, page 11-21
  • ISSN: 0073-8301

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Bourgain, Jean. "On nonlinear Schrödinger equations." Publications Mathématiques de l'IHÉS S88 (1998): 11-21. <http://eudml.org/doc/104139>.

@article{Bourgain1998,
author = {Bourgain, Jean},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {nonlinear Schrödinger equations; global solutions; invariant tori; bounded spacial domain},
language = {eng},
pages = {11-21},
publisher = {Institut des Hautes Etudes Scientifiques},
title = {On nonlinear Schrödinger equations},
url = {http://eudml.org/doc/104139},
volume = {S88},
year = {1998},
}

TY - JOUR
AU - Bourgain, Jean
TI - On nonlinear Schrödinger equations
JO - Publications Mathématiques de l'IHÉS
PY - 1998
PB - Institut des Hautes Etudes Scientifiques
VL - S88
SP - 11
EP - 21
LA - eng
KW - nonlinear Schrödinger equations; global solutions; invariant tori; bounded spacial domain
UR - http://eudml.org/doc/104139
ER -

References

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  1. [B1] J. Bourgain , Global wellposedness of defocusing 3D critical NLS in the radial case, JAMS, to appear. 
  2. [B2] J. Bourgain , Periodic nonlinear Schrödinger equation and Invariant Measures, CMP, Vol. 166, N1 (1994), 1-26. Zbl0822.35126MR1309539
  3. [B3] J. Bourgain , Invariant measures for the 2D-defocusing nonlinear Schrödinger equation, CMP176 (1996), 421-445. Zbl0852.35131MR1374420
  4. [B4] J. Bourgain , Invariant measures for the Gross-Piateskii equation , J. Math Pures Appl.76, 1997, 649-702. Zbl0906.35095MR1470880
  5. [B5] J. Bourgain , Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Annals of Math, (to appear). Zbl0928.35161MR1668547
  6. [B6] J. Bourgain , Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations, GAFA, Vol. 6, N2 (1996), 201-230. Zbl0872.35007MR1384610
  7. [Ca-We] T. Cazenave , F. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in HS, Nonlinear Anal., TMA 14 (1990), 807-836. Zbl0706.35127MR1055532
  8. [Cr-Wa] W. Craig, G. Wayne, Newton's method and periodic solutions of nonlinear wave equations , CPAM46 ( 1993 ),1409-1501. Zbl0794.35104
  9. [GV] J. Ginibre , G. Velo, On a class of nonlinear Schrödinger equations I, II, III, JFA32 ( 1979),1-71; Ann. Inst. H. Poincaré - Phys. Th.28 (1978), 287-316. Zbl0397.35012MR498408
  10. [F-S-Wi] J. Fröhlich , T. Spencer, P. Wittwer, Localization for a class of one dimensional quasi-periodic Schrödinger operators, CMP132, N1 (1990), 5-25. Zbl0722.34070MR1069198
  11. [F-S-Wa] J. Fröhlich , T. Spencer, E. Wayne, Localization in disordered, nonlinear dynamical systems, J. Stat. Ph.42 (1986), 257-275. Zbl0629.60105MR833019
  12. [Ja] A. Jaffe, Notes (1994). 
  13. [K] S. Kuksin , Nearly integrable infinite-dimensional Hamiltonian systems, LNM1556, Springer. Zbl0784.58028
  14. [K-P] S. Kuksin , J. Poschel, Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation, Annals of Math143:1 (1996), 149-179. Zbl0847.35130MR1370761
  15. [B-S] D. Brydges , G. Slade, Statistical mechanics of the 2-dimensional focusing nonlinear Schrödinger equation, CMP ( 1996) 182, 485-504. Zbl0867.35090MR1447302
  16. [L-R-S, 1, 2] J. Lebowitz, H. Rose, E. Speer, Statistical mechanics of the nonlinear Schrödinger equation, J. Stat. Phys.50 (1988), 657-687. Idem, Mean field approximation , J. Stat. Phys.54 ( 1989), 17-56. Zbl0850.35110MR984249

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