Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 11, 11 p.
@article{SEDP_2004-2005____A11_0,
     author = {Wang, Wei-Min},
     title = {Quasi {Periodic} {Solutions} of {Nonlinear} {Random} {Schr\"odinger} {Equations}},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:11},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2004-2005},
     mrnumber = {2182056},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2004-2005____A11_0/}
}
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Wang, Wei-Min. Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 11, 11 p. http://www.numdam.org/item/SEDP_2004-2005____A11_0/

[AF] Albanese, C.; Fröhlich, J. Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations I, Commun. Math. Phys., Volume 116 (1988), pp. 475-502 | MR 937771 | Zbl 0696.35185

[AFHS] Aizenman, M.; Friedrich, R.; Hundertmark, D.; Shankar, S. Constructive fractional-moment criteria for localization in random operators, Phys. A, Volume 279 (2000), pp. 369-377 | MR 1797147

[AFS] Albanese, C.; Fröhlich, J.; Spencer, T. Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations II, Commun. Math. Phys., Volume 119 (1988), pp. 677-699 | MR 973022 | Zbl 0699.35242

[AM] Aizenman, M.; Molchanov, S. Localization at large disorder and at extreme energies: an elementary derivation, Commun. Math. Phys., Volume 157 (1993), pp. 245 | MR 1244867 | Zbl 0782.60044

[An] Anderson, P. Absence of diffusion in certain random lattices, Phys.Rev., Volume 109 (1958), pp. 1492

[B1] Bourgain, J. Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, IMRN, Volume 11 (1994), pp. 475-497 | MR 1316975 | Zbl 0817.35102

[B2] Bourgain, J. Construction of approximate and almost periodic solutions of perturbed linear Schrödinger and wave equations, GAFA, Volume 6 (1996), pp. 201-230 | MR 1384610 | Zbl 0872.35007

[B3] Bourgain, J. Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Ann. Math, Volume 148 (1998), pp. 363-439 | MR 1668547 | Zbl 0928.35161

[B4] Bourgain, J. Nonlinear Schrödinger equations, Park City Lectures, 1999 | MR 1662829 | Zbl 0952.35127

[B5] Bourgain, J. Green’s function estimates for latttice Schrödinger operators and applications, Lectures at UC, Irvine and UCLA, 2000-2001

[Ba] Basu, S. On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets, Discrete Comput. Geom., Volume 22 (1999), pp. 1-18 | MR 1692627 | Zbl 0973.14033

[BGS] Bourgain, J.; Goldstein, M.; Schlag, W. Anderson localization for Schrödinger operators on 2 with quasi-periodic potential, Acta Math., Volume 188 (2002), pp. 41-86 | MR 1947458 | Zbl 1022.47023

[BW1] Bourgain, J.; Wang, W.-M. Anderson localization for time quasi-periodic random Schrödinger and wave equations, Commun. Math. Phys., Volume 248 (2004), pp. 429-466 | MR 2076917

[BW2] Bourgain, J.; Wang, W.-M. Quasi periodic solutions of nonlinear random Schrödinger equations, (submitted) (2004)

[BW3] Bourgain, J.; Wang, W.-M. Diffusion bound for a nonlinear Schrödinger equation, (preprint) (2004) | MR 2333206

[CFKS] Cycon, H. L.; Froese, R. G.; Kirsch, W.; Simon, B. Schrödinger Operators, Springer-Verlag, 1987 | MR 883643 | Zbl 0619.47005

[CP] Chierchia, L.; Perfetti, P. Maximal almost-periodic solutions for Lagrangian equations on infinite dimensional tori, Seminar on Dynamical Systems. Eds. S. Kuksin, V. Lazutkin, J. Pöschel. Birkhäuser, Basel (1994), pp. 203-212 | MR 1279399 | Zbl 0796.34028

[CW1] Craig, W.; Wayne, C. E. Newton’s method and periodic solutions of nonlinear equations, Commun. Pure Appl. Math., Volume 46 (1993), pp. 1409-1498 | Zbl 0794.35104

[CW2] Craig, W.; Wayne, C. E. Periodic solutions of nonlinear Schrödinger equations and the Nash-Moser method, Hamiltonian Mechanics, 103-122, Nato Adv. Sci. Inst. Ser. B Phys. 331, Plenum, NY, 1994 | MR 1316671

[E] Eliasson, L. H. Perturbations of stable invariant tori for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa CI. Sci, Volume 15 (1988), pp. 115-147 | Numdam | MR 1001032 | Zbl 0685.58024

[FMSS] Fröhlich, J.; Martinelli, F.; Scoppola, E.; Spencer, T. Constructive proof of localization in Anderson tight binding model, Commun. Math. Phys., Volume 101 (1985), pp. 21-46 | MR 814541 | Zbl 0573.60096

[FS] Fröhlich, J.; Spencer, T. Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Commun. Math. Phys., Volume 88 (1983), pp. 151-184 | MR 696803 | Zbl 0519.60066

[FSW] Fröhlich, J.; Spencer, T.; Wayne, C. E. Localization in disordered, nonlinear dynamical systems, J. Stat. Phys., Volume 42 (1986), pp. 247-274 | MR 833019 | Zbl 0629.60105

[GMP] Gol’dsheid, Ya.; Molchanov, S.; Pastur, L. Pure point spectrum of stochastic one dimensional Schrödinger operators, Func. Anal. Appl, Volume 11, 1 (1977) | Zbl 0368.34015

[KP] Kuksin, S.; Pöschel, J. Invariant Cantor manifolds of quasi-periodic osillations for a nonlinear Schrödinger equation, Ann. Math., Volume 143 (1996), pp. 149-179 | MR 1370761 | Zbl 0847.35130

[Le] Levin, Ya. B. Lectures on Entire Functions, Transl. of Math. Monographs, vol. 150, AMS, Providence, RI, 1996 | MR 1400006 | Zbl 0856.30001

[LL] Lieb, E. H.; de Llano, M. Solitons and the delta function fermion gas in the Hartree-Fock theory, J. Math. Phys., Volume 19 (1978), pp. 860

[LZ] Levitan, B. M.; Zhikov, V. V. Almost-Periodic Functions and Differential Equations, von Nostrand Reinhold, NY, 1971

[O] Overhauser, A. W. Structure of nuclear matter, Phys. Rev. Lett., Volume 4 (1960), pp. 415 | Zbl 0091.23005

[PF] Pastur, L.; Figotin, A. Spectra of Random and Almost Periodic Operators, Springer, 1992 | MR 1223779 | Zbl 0752.47002

[Pö1] Pöschel, J. Small divisors with spatial structure in infinite dimensional Hamiltonian systems, Commun. Math. Phys., Volume 127 (1990), pp. 351-393 | MR 1037110 | Zbl 0702.58065

[Pö2] Pöschel, J. On the construction of almost periodic solutions for a nonlinear Schrödinger equation, Ergod. Th. and Dynam. Sys., Volume 22 (2002), pp. 1537-1549 | MR 1934149 | Zbl 1020.37044

[S] Shastry, B. Sriram Exact solutions of a nonlinear eigenvalue problem in one dimension, Phys. Rev. Lett., Volume 50 (1983), pp. 633 | MR 700922

[vDK] von Dreifus, H.; Klein, A. A new proof of localization in the Anderson tight binding model, Commun. Math. Phys., Volume 124 (1989), pp. 285-299 | MR 1012868 | Zbl 0698.60051

[W] Wayne, C. E. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Commun. Pure Appl. Math., Volume 127 (1990), pp. 479-528 | MR 1040892 | Zbl 0708.35087