@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}, pages = {1--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/} }
TY - JOUR AU - Wang, Wei-Min TI - Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:11 PY - 2004-2005 SP - 1 EP - 11 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2004-2005____A11_0/ LA - en ID - SEDP_2004-2005____A11_0 ER -
%0 Journal Article %A Wang, Wei-Min %T Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:11 %D 2004-2005 %P 1-11 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2004-2005____A11_0/ %G en %F SEDP_2004-2005____A11_0
Wang, Wei-Min. Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Talk no. 11, 11 p. http://www.numdam.org/item/SEDP_2004-2005____A11_0/
[AF] 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 | Zbl
[AFHS] Constructive fractional-moment criteria for localization in random operators, Phys. A, Volume 279 (2000), pp. 369-377 | MR
[AFS] 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 | Zbl
[AM] Localization at large disorder and at extreme energies: an elementary derivation, Commun. Math. Phys., Volume 157 (1993), pp. 245 | MR | Zbl
[An] Absence of diffusion in certain random lattices, Phys.Rev., Volume 109 (1958), pp. 1492
[B1] Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, IMRN, Volume 11 (1994), pp. 475-497 | MR | Zbl
[B2] Construction of approximate and almost periodic solutions of perturbed linear Schrödinger and wave equations, GAFA, Volume 6 (1996), pp. 201-230 | MR | Zbl
[B3] Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Ann. Math, Volume 148 (1998), pp. 363-439 | MR | Zbl
[B4] Nonlinear Schrödinger equations, Park City Lectures, 1999 | MR | Zbl
[B5] Green’s function estimates for latttice Schrödinger operators and applications, Lectures at UC, Irvine and UCLA, 2000-2001
[Ba] On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets, Discrete Comput. Geom., Volume 22 (1999), pp. 1-18 | MR | Zbl
[BGS] Anderson localization for Schrödinger operators on with quasi-periodic potential, Acta Math., Volume 188 (2002), pp. 41-86 | MR | Zbl
[BW1] Anderson localization for time quasi-periodic random Schrödinger and wave equations, Commun. Math. Phys., Volume 248 (2004), pp. 429-466 | MR
[BW2] Quasi periodic solutions of nonlinear random Schrödinger equations, (submitted) (2004)
[BW3] Diffusion bound for a nonlinear Schrödinger equation, (preprint) (2004) | MR
[CFKS] Schrödinger Operators, Springer-Verlag, 1987 | MR | Zbl
[CP] 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 | Zbl
[CW1] Newton’s method and periodic solutions of nonlinear equations, Commun. Pure Appl. Math., Volume 46 (1993), pp. 1409-1498 | Zbl
[CW2] 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
[E] Perturbations of stable invariant tori for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa CI. Sci, Volume 15 (1988), pp. 115-147 | Numdam | MR | Zbl
[FMSS] Constructive proof of localization in Anderson tight binding model, Commun. Math. Phys., Volume 101 (1985), pp. 21-46 | MR | Zbl
[FS] 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 | Zbl
[FSW] Localization in disordered, nonlinear dynamical systems, J. Stat. Phys., Volume 42 (1986), pp. 247-274 | MR | Zbl
[GMP] Pure point spectrum of stochastic one dimensional Schrödinger operators, Func. Anal. Appl, Volume 11, 1 (1977) | Zbl
[KP] Invariant Cantor manifolds of quasi-periodic osillations for a nonlinear Schrödinger equation, Ann. Math., Volume 143 (1996), pp. 149-179 | MR | Zbl
[Le] Lectures on Entire Functions, Transl. of Math. Monographs, vol. 150, AMS, Providence, RI, 1996 | MR | Zbl
[LL] Solitons and the delta function fermion gas in the Hartree-Fock theory, J. Math. Phys., Volume 19 (1978), pp. 860
[LZ] Almost-Periodic Functions and Differential Equations, von Nostrand Reinhold, NY, 1971
[O] Structure of nuclear matter, Phys. Rev. Lett., Volume 4 (1960), pp. 415 | Zbl
[PF] Spectra of Random and Almost Periodic Operators, Springer, 1992 | MR | Zbl
[Pö1] Small divisors with spatial structure in infinite dimensional Hamiltonian systems, Commun. Math. Phys., Volume 127 (1990), pp. 351-393 | MR | Zbl
[Pö2] On the construction of almost periodic solutions for a nonlinear Schrödinger equation, Ergod. Th. and Dynam. Sys., Volume 22 (2002), pp. 1537-1549 | MR | Zbl
[S] Exact solutions of a nonlinear eigenvalue problem in one dimension, Phys. Rev. Lett., Volume 50 (1983), pp. 633 | MR
[vDK] A new proof of localization in the Anderson tight binding model, Commun. Math. Phys., Volume 124 (1989), pp. 285-299 | MR | Zbl
[W] Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Commun. Pure Appl. Math., Volume 127 (1990), pp. 479-528 | MR | Zbl