W. Bao, N. B. Abdallah, and Y. Cai, Gross???Pitaevskii???Poisson Equations for Dipolar Bose???Einstein Condensate with Anisotropic Confinement, SIAM Journal on Mathematical Analysis, vol.44, issue.3, pp.1713-1741, 2012.
DOI : 10.1137/110850451

URL : https://hal.archives-ouvertes.fr/hal-00848951

W. Bao and Y. Cai, Mathematical theory and numerical methods for Bose-Einstein condensation, Kinetic and Related Models, vol.6, issue.1, pp.1-135, 2013.
DOI : 10.3934/krm.2013.6.1

W. Bao, Y. Cai, and H. Wang, Efficient numerical methods for computing ground states and dynamics of dipolar Bose???Einstein condensates, Journal of Computational Physics, vol.229, issue.20, pp.7874-7892, 2010.
DOI : 10.1016/j.jcp.2010.07.001

URL : https://hal.archives-ouvertes.fr/hal-01273317

W. Bao, L. L. Treust, and F. Méhats, Dimension reduction for anisotropic Bose???Einstein condensates in the strong interaction regime, Nonlinearity, vol.28, issue.3, 1403.
DOI : 10.1088/0951-7715/28/3/755

URL : https://hal.archives-ouvertes.fr/hal-00959084

N. B. Abdallah, Y. Cai, C. Castella, and F. Méhats, Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential, Kinet. Relat. Models, vol.4, pp.831-856, 2011.

N. B. Abdallah, F. Castella, and F. Méhats, Time averaging for the strongly confined nonlinear Schr??dinger equation, using almost-periodicity, Journal of Differential Equations, vol.245, issue.1, pp.154-200, 2008.
DOI : 10.1016/j.jde.2008.02.002

Y. Cai, M. Rosenkranz, Z. Lei, and B. Bao, Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions, Physical Review A, vol.82, issue.4, p.43623, 2010.
DOI : 10.1103/PhysRevA.82.043623

R. Carles, Semi-classical analysis for nonlinear Schrödinger equations, World Scientific, 2008.

R. Carles, P. A. Markowich, and C. Sparber, On the Gross???Pitaevskii equation for trapped dipolar quantum gases, Nonlinearity, vol.21, issue.11, pp.2569-2590, 2008.
DOI : 10.1088/0951-7715/21/11/006

URL : https://hal.archives-ouvertes.fr/hal-00277453

T. Cazenave, Semilinear Schrödinger equations, AMS Bookstore, vol.10, 2003.

A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, and T. Pfau, Bose-Einstein Condensation of Chromium, Physical Review Letters, vol.94, issue.16, p.94, 2005.
DOI : 10.1103/PhysRevLett.94.160401

B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques. Société mathématique de France, 1984.

L. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Reports on Progress in Physics, vol.72, issue.12, p.126401, 2009.
DOI : 10.1088/0034-4885/72/12/126401

URL : https://hal.archives-ouvertes.fr/hal-00909915

M. Lu, N. Q. Burdick, S. H. Youn, and B. H. Lev, Strongly Dipolar Bose-Einstein Condensate of Dysprosium, Physical Review Letters, vol.107, issue.19, 2011.
DOI : 10.1103/PhysRevLett.107.190401

C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, 2002.

M. Rosenkranz, Y. Cai, and W. Bao, Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates, Physical Review A, vol.88, issue.1, p.13616, 2013.
DOI : 10.1103/PhysRevA.88.013616

L. Santos, G. Shlyapnikov, P. Zoller, and M. Lewenstein, Bose-Einstein Condensation in Trapped Dipolar Gases, Physical Review Letters, vol.85, issue.9, pp.1791-1797, 2000.
DOI : 10.1103/PhysRevLett.85.1791

S. Yi and L. You, Trapped atomic condensates with anisotropic interactions, Physical Review A, vol.61, issue.4, p.41604, 2000.
DOI : 10.1103/PhysRevA.61.041604

S. Yi and L. You, Trapped condensates of atoms with dipole interactions, Physical Review A, vol.63, issue.5, p.53607, 2001.
DOI : 10.1103/PhysRevA.63.053607