G. Akrivis, Finite difference discretization of the cubicSchrödinger equation, IMA J. Numer. Anal, vol.13, pp.115-124, 1993.

W. Bao, D. Jaksch, and P. A. Markowich, Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation, J. Comp. Phys, vol.187, pp.318-342, 2003.

W. Bao, P. A. Markowich, C. Schmeiser, and R. M. , On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments, Math. Models Meth. Appl. Sci, vol.15, issue.5, pp.767-782, 2005.

W. Bao and J. Shen, A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates, SIAM J. Sci. Comput, vol.26, pp.2020-2028, 2005.

W. Bao and J. Shen, A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates, J. Comput. Phys, vol.227, pp.9778-9793, 2008.

N. B. Abdallah, F. Castella, and F. Méhats, Time averaging for the strongly confined nonlinear Schrödinger equation, using almost periodicity, J. Differential Equations, vol.245, pp.154-200, 2008.

N. B. Abdallah, F. Méhats, and O. Pinaud, The adiabatic approximation of the Schröinger Poisson system with a partial confinement, SIAM J. Math. Anal, vol.36, pp.986-1013, 2005.

N. B. Abdallah, F. Méhats, C. Schmeiser, and R. M. , The nonlinear Schrödinger equation with strong anisotropic harmonic potential, SIAM J. Math. Anal, vol.37, issue.1, pp.189-199, 2005.

B. Bidéaray, F. Castella, and P. Degond, From Bloch model to the rate equations, Discrete Contin, Dyn. Syst, vol.11, pp.1-26, 2004.

B. Bidéaray-fesquet, F. Castella, E. Dumas, and M. Gisclon, From Bloch model to the rate equations, II: The case of almost degenerate energy levels, Math. Models Methods Appl. Sci, vol.14, pp.1785-1817, 2004.

J. M. Bony and J. Y. Chemin, Espaces fonctionnels associés au calcul de Weyl- Hörmander, Bull. Soc. Math. France, vol.122, pp.77-118, 1994.

B. M. Caradoc-davis, R. J. Ballagh, and K. Burnett, Coherent dynamics of vortex formation in trapped Bose-Einstein condensates, Phys. Rev. Lett, vol.83, pp.895-898, 1999.

F. Castella, P. Degond, and T. Goudon, Diffusion dynamics of classical systems driven by an oscillatory force, J. Stat. Phys, vol.124, pp.913-950, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00449422

F. Castella, P. Degond, and T. Goudon, Large time dynamics of a classical system subject to a fast varying force, Comm. Math. Phys, vol.276, pp.23-49, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00365201

T. Cazenave, Semilinear Schrödinger equations, Courant Lect. Notes Math, vol.10, 2003.

F. Delebecque-fendt and F. Méhats, An effective mass theorem for the bidimensional electron gas in a strong magnetic field, Comm. Math. Phys, vol.292, pp.829-870, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00378528

C. M. Dion and E. Cances, Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap, Phys. Rev. E, p.67, 2003.

D. Funaro, Polynomial approximations of differential equations, 1992.

E. Grenier, Oscillatory perturbations of the NavierCStokes equations, J. Math. Pures Appl, vol.76, pp.477-498, 1997.

R. H. Hardin and F. D. Tappert, Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations, SIAM Rev, Chronicle, pp.15-423, 1973.

B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Astérisque, p.112, 1984.

B. Helffer and F. Nier, Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians, Lecture Notes in Math, vol.1862, 2005.
DOI : 10.1007/b104762

URL : http://link.springer.com/content/pdf/bfm%3A978-3-540-31553-7%2F1.pdf

D. Lannes, Nonlinear geometrical optics for oscillatory wave trains with a continuous oscillatory spectrum, Adv. Differential Equations, vol.6, pp.731-768, 2001.

G. Métivier and S. Schochet, Averaging theorems for conservative systems and the weakly compressible Euler equations, J. Differential Equations, vol.187, pp.106-183, 2003.

M. P. Robinson, G. Fairweather, and B. M. Herbst, On the numerical solution of the cubic Schrödinger equation in one space variable, J. Comput. Phys, vol.104, pp.277-284, 1993.

J. A. Sanders and F. Verhulst, Averaging methods in nonlinear dynamical systems, Appl. Math. Sci, vol.59, 1985.

S. Schochet, Fast singular limits of hyperbolic PDEs, J. Differential Equations, vol.114, pp.476-512, 1994.

T. R. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations, II. Numerical, nonlinear Schrödinger equation, J. Comput. Phys, vol.55, pp.203-230, 1984.