Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, vol.269, pp.198-201, 1995. ,
Computational methods for the dynamics of nonlinear Schrödinger and Gross-Pitaevskii equations, (A Feature Article), Comp. Phys. Comm, vol.184, issue.12, pp.2621-2633, 2013. ,
High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations, J. Comput. Phys, vol.327, issue.15, pp.252-269, 2016. ,
Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates, J. Comput. Phys, vol.258, pp.509-523, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00931117
Modeling and computation of Bose-Einstein Condensates: stationary states, nucleation, dynamics, stochasticity, Nonlinear Optical and Atomic Systems: at the Interface of Mathematics and Physics, pp.49-145, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01094826
Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method, J. Comput. Phys, vol.343, pp.92-109, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01393094
Mathematical theory and numerical methods for Bose-Einstein condensation, Kinet. Relat. Mod, vol.6, pp.1-135, 2013. ,
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation, Math. Comput, vol.82, pp.99-128, 2013. ,
Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation, SIAM J. Appl. Math, vol.66, pp.758-786, 2006. ,
Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation, SIAM J. Numer. Anal, vol.57, pp.657-680, 2019. ,
Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation, J. Comput. Phys, vol.187, pp.318-342, 2003. ,
A simple and efficient numerical method for computing the dynamics of rotating Bose-Einstein Condensates via rotating lagrangian coordinates, SIAM J. Sc. Comput, vol.35, issue.6, pp.2671-2695, 2013. ,
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates, SIAM J. Sci. Comput, vol.26, pp.2020-2028, 2005. ,
Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation, J. Comput. Phys, vol.235, pp.423-445, 2013. ,
An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates, J. Comput. Phys, vol.217, pp.612-626, 2006. ,
A relaxation scheme for the nonlinear Schrödinger equation, SIAM J. Numer. Anal, vol.42, pp.934-952, 2004. ,
Dujardin and I. Lacroix-Violet, Energy preserving methods for nonlinear Schrödinger equations, IMA Journal of Numerical Analysis ,
Structure-preserving algorithms for the two dimensional sine-Gordon equation with Neumann boundary conditions, J. Comput. Phys, vol.395, pp.166-185, 2019. ,
High-order time-splitting Hermite and Fourier spectral methods for the Gross-Pitaevskii equation, J. Comput. Phys, vol.228, pp.822-832, 2009. ,
A new Lagrange multiplier approach for gradient flows, Comput. Methods Appl. Mech. Engrg, vol.367, p.13070, 2020. ,
Global constraints preserving scalar auxiliary variable schemes for gradient flows, SIAM J. Sci. Comput, vol.42, pp.2514-2536, 2020. ,
Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach, J. Sci. Comput, vol.78, pp.1467-1487, 2019. ,
Energy-dependent effective interactions for dilute many-body systems, Phys. Rev. A, vol.75, p.13615, 2007. ,
Finite-difference solutions of a nonlinear Schrödinger equation, J. Comput. Phys, vol.44, pp.277-288, 1981. ,
Validity of the shape-independent approximation for Bose-Einstein condensates, Phys. Rev. A, vol.60, pp.1451-1462, 1999. ,
High-order mass-and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation ,
Rotating trapped Bose-Einstein condensates, Rev. Mod. Phys, vol.81, pp.647-691, 2009. ,
Structure of a quantized vortex in boson systems, Nuovo. Cimento, vol.20, pp.454-457, 1961. ,
Dark and bright soliton exchange in a nonlinear dispersive medium, J. Korean Phys. Society, vol.38, pp.558-561, 2001. ,
Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable, J. Comput. Phys, vol.388, pp.1-22, 2019. ,
Mass and energy conservative high-order schemes for the nonlinear Schrödinger equation in one and two dimensions, 2019. ,
Pseudo-spectral solution of nonlinear Schrödinger equation, J. Comput. Phys, vol.87, pp.108-125, 1990. ,
Vortex lines in an imperfect Bose gas, Soviet Phys. JETP, vol.13, pp.451-454, 1961. ,
, Bose-Einstein Condensation, 2003.
Self-action of light beams in nonlinear media: soliton solutions, Opt. Quantum Electron, vol.11, pp.471-478, 1979. ,
Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions, J. Phys. B: At. Mol. Opt. Phys, vol.49, p.125304, 2016. ,
Iterative Methods for Sparse Linear Systems, 1996. ,
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput, vol.7, issue.3, pp.856-869, 1986. ,
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows, SIAM J. Numer. Anal, vol.56, pp.2895-2912, 2018. ,
The scalar auxiliary variable (SAV) approach for gradient flows, J. Comput. Phys, vol.352, pp.407-417, 2018. ,
A new class of efficient and robust energy stable schemes for gradient flows, SIAM Review, pp.474-506, 2019. ,
Efficient SAV approach for imaginary time gradient flows with applications to one-and multi-component Bose-Einstein Condensates, J. Comput. Phys, vol.396, pp.72-88, 2019. ,
High-order exponential operator splitting methods for time-dependent Schrödinger equations, SIAM J. Numer. Anal, vol.46, pp.2022-2038, 2008. ,
Convergence analysis of high-order time-splitting pseudo-spectral methods for nonlinear Schrödinger equations, SIAM J. Numer. Anal, vol.50, pp.3231-3258, 2012. ,
A time-splitting spectral method for coupled Gross-Pitaevskii equations with applications to rotating Bose-Einstein condensates, J. Comput. Appl. Math, vol.205, pp.88-104, 2007. ,
Split-step methods for the solution of the nonlinear Schrödinger equation, SIAM J. Numer. Anal, vol.23, pp.485-507, 1986. ,