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Articles to be published soon

  • Numerical analysis of the Gross-Pitaevskii Equation with a randomly varying potential in time
    Romain Poncet
    to appear in IMA Journal of Numerical Analysis.
    Preprint

  • Universal dynamics for the defocusing logarithmic Schrödinger equation
    Rémi Carles, Isabelle Gallagher
    to appear in Duke Mathematical Journal.
    Preprint

  • On the Numerical Solution and Dynamical Laws of Nonlinear Fractional Schrödinger/Gross-Pitaevskii Equations
    Xavier Antoine, Qinglin Tang, Jiwei Shang
    to appear in Journal of Computer Mathematics.
    Preprint

Articles published in 2017

  • Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations
    Xavier Antoine, Christophe Besse, Vittorio Rispoli
    Computer Physics Communications 219 (2017), pp. 70-78.
    Article - Preprint

  • High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates
    Christophe Besse, Guillaume Dujardin, Ingrid Lacroix-Violet
    SIAM Journal of Numerical Analysis 55-3 (2017), pp. 1387-1411.
    Article - Preprint

  • An Analysis of Schwarz Waveform Relaxation Domain Decomposition Methods for the Imaginary-Time Linear Schrödinger and Gross-Pitaevskii Equations
    Xavier Antoine, Emmanuel Lorin
    Numerische Mathematik 137-4 (2017), pp. 923-958.
    Article - Preprint

  • Computation of Ground States of the Gross-Pitaevskii Functional via Riemannian Optimization
    Ionut Danaila, Bartosz Protas
    SIAM Journal on Scientific Computing 39-6 (2017), pp. B1102-B1129.
    Article - Preprint

  • Multiple Positive Standing Wave Solutions for Schrödinger Equations with Oscillating State-Dependent Potentials
    Renata Bunoiu, Radu Precup, Csaba Varga
    Communications on Pure and Applied Analysis 16-3 (2017), pp. 954-972.
    Article - Preprint

  • On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity
    Rémi Carles, Clément Gallo
    Numerische Mathematik 136-1 (2017), pp. 315-342.
    Article - Preprint

  • Restoring quasireversibility with a single topological charge
    Juan-Pablo Álvarez Zúñiga, Christophe Besse, Romain Duboscq, Juliette Billy, David Guéry-Odelin
    Physical Review A 96-5 (2017), 053618.
    Article - Preprint

  • Domain decomposition algorithms for two dimensional linear Schrödinger equation
    Christophe Besse, Feng Xing
    Journal of Scientific Computing 72-2 (2017), pp. 735-760.
    Article - Preprint

  • Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective
    Rémi Carles, Anne Nouri
    Journal Asymptotic Analysis 102 (2017), pp. 99-117.
    Article - Preprint

  • WKB analysis of generalized derivative nonlinear Schrödinger equations without hyperbolicity
    Rémi Carles, Clément Gallo
    Mathematical Models and Methods in Applied Sciences 27-9 (2017), pp. 1727-1742.
    Article - Preprint

  • Efficient Spectral Computation of the Stationary States of Rotating Bose-Einstein Condensates by the Preconditioned Nonlinear Conjugate Gradient Method
    Xavier Antoine, Antoine Levitt, Qinglin Tang
    Journal of Computational Physics 343 (2017), pp. 92-109.
    Article - Preprint

  • An Analysis of Schwarz Waveform Relaxation Domain Decomposition Methods for the Imaginary-Time Linear Schrödinger and Gross-Pitaevskii Equations
    Xavier Antoine, Emmanuel Lorin
    Numerische Mathematik 137-4 (2017), pp. 923-958.
    Article - Preprint

  • A Friendly Review of Absorbing Boundary Conditions and Perfectly Matched Layers for Classical and Relativistic Quantum Waves Equations
    Xavier Antoine, Emmanuel Lorin, Qinglin Tang
    Molecular Physics 115-15-16 (2017), pp. 1861-1879.
    Article - Preprint

Articles published in 2016

  • IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger / Gross-Pitaevskii equations
    Xavier Antoine, Christophe Besse, Vittorio Rispoli
    Journal of Computational Physics 327 (2016), pp. 252-269.
    Article - Preprint

  • Analysis of a time-splitting scheme for a class of random nonlinear partial differential equations
    Romain Duboscq, Renaud Marty
    ESAIM: Probability and Statistics 20 (2016), pp. 572-589.
    Article - Preprint

  • Vector Dark-Antidark Solitary Waves in Multi-Component Bose-Einstein condensates
    Ionut Danaila, Amin Khamehchi, Vandna Gokhroo, Peter Engels, Panayotis Kevrekidis
    Physical Review Letters A 94 (2016), pp. 053617
    Article - Preprint

  • A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
    Guillaume Vergez, Ionut Danaila, Sylvain Auliac, Frédéric Hecht
    Computer Physics Communications 209 (2016), pp. 144-162
    Article - Preprint

  • The ground state of two coupled Gross–Pitaevskii equations in the Thomas–Fermi limit
    Clément Gallo
    Journal de Mathématiques Pures et Appliquées 106(1) (2016), pp. 1-75.
    Article - Preprint

  • A construction of the fundamental solution of the Schrödinger equation with a perturbed quadratic Hamiltonian
    Romain Duboscq
    Nonlinearity 29(2) (2016), pp. 566-602.
    Article - Preprint

  • Schwarz waveform relaxation method for one dimensional Schrödinger equation with general potential
    Christophe Besse, Feng Xing
    Numerical Algorithms 74-2 (2016), pp. 393-426.
    Article - Preprint

  • On semi-classical limit of nonlinear quantum scattering
    Rémi Carles
    Annales Scientifiques de l'École Normale Supérieure 49(4) (2016), pp. 711-756.
    Article - Preprint

  • Lagrange-Schwarz Waveform Relaxation Domain Decomposition Methods for Linear and Nonlinear Quantum Wave Problems
    Xavier Antoine, Emmanuel Lorin
    Applied Mathematics Letters 57 (2016), pp. 38-45.
    Article - Preprint

  • On the Ground States and Dynamics of Space Fractional Nonlinear Schrödinger/Gross-Pitaevskii Equations with Rotation Term and Nonlocal Nonlinear Interactions
    Xavier Antoine, Qinglin Tang, Yong Zhang
    Journal of Computational Physics 325 (2016), pp. 74-97.
    Article - Preprint

  • Frozen Gaussian Approximation based Domain Decomposition Methods for the Linear and Nonlinear Schrödinger Equation Beyond the Semi-Classical Regime
    Emmanuel Lorin, Xu Yang, Xavier Antoine
    Journal of Computational Physics 315 (2016), pp. 221-237.
    Article - Preprint

  • Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates
    Christophe Besse, Feng Xing
    SMAI Journal of Computational Mathematics 2 (2016), pp. 277-300.
    Article - Preprint

Articles published in 2015

  • Higher order Schrödinger and Hartree-Fock equations
    Rémi Carles, Wolfgang Lucha and Emmanuel Moulay
    Journal of Mathematical Physics 56(12) (2015), 122301.
    Article - Preprint

  • Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement
    Rémi Carles, Clément Gallo
    Journal of Mathematical Physics 56-10 (2015), 101503.
    Article - Preprint

  • GPELab, a Matlab Toolbox to solve Gross-Pitaevskii Equations II: dynamics and stochastic simulations
    Xavier Antoine, Romain Duboscq
    Computer Physics Communications 193 (2015), pp. 95-117.
    Article - Preprint

  • Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases
    Rémi Carles, Hichem Hajaiej
    Bulletin of the London Mathematical Society 47(3) (2015), pp. 509-518.
    Article - Preprint

  • Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential
    Rémi Carles
    Zeitschrift für angewandte Mathematik und Physik 66(4) (2015), pp. 2087-2094.
    Article - Preprint

  • Vortex solutions in BEC under a trapping potential varying randomly in time
    Anne de Bouard, Reika Fukuizumi, Romain Poncet
    Discrete and Continuous Dynamical Systems, series B 20(9) (2015), pp. 2793-2817.
    Article - Preprint

  • Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
    Weizhu Bao, Shidong Jiang, Qinglin Tang, Yong Zhang
    Journal of Computational Physics 296 (2015), pp. 72-89.
    Article - Preprint

  • Vortex dynamics of rotating Bose-Einstein condensate of microcavity polaritons
    Bikash Padhi, Romain Duboscq, Ankita Niranjan, Ravi K. Soni
    The European Physical Journal B, May 2015, pp. 88-116.
    Article

  • Vectorial approach to coupled nonlinear Schrödinger systems under nonlocal Cauchy conditions
    Renata Bunoiu, Radu Precup
    Applicable Analysis 95(4) (2015), pp. 731-747.
    Article - Preprint

  • Finite time extinction for nonlinear Schrödinger equation in 1D and 2D
    Rémi Carles, Tohru Ozawa
    Partial Differential Equations 40(5) (2015), pp. 897-917.
    Article - Preprint

  • On Nonlinear Schrödinger-Type Equations with Nonlinear Damping
    Paolo Antonelli, Rémi Carles, Christof Sparber
    International Mathematical Research Notices (2015), pp. 740-762.
    Article - Preprint

  • Scattering for nonlinear Schrödinger equation under partial harmonic confinement
    Paolo Antonelli, Rémi Carles, Jorge Drumond Silva
    Communications in Mathematical Physics 334(1) (2015), pp.367-396.
    Article - Preprint

  • Domain Decomposition Methods and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrödinger Equation with Ionization and Recombination by Intense Electric Field
    Xavier Antoine, Emmanuel Lorin, André D. Bandrauk
    Journal of Scientific Computing 64(3) (2015), pp. 620-646.
    Article - Preprint

Articles published in 2014

  • GPELab, a Matlab Toolbox to solve Gross-Pitaevskii Equations I: computation of stationary solutions
    X. Antoine, Romain Duboscq
    Computer Physics Communications 185(11) (2014), pp. 2969-2991.
    Article - Preprint

  • Robust and efficient preconditioned Krylov spectral solvers for computing the ground states and dynamics of fast rotating and strongly interacting Bose-Einstein condensates
    Xavier Antoine, Romain Duboscq
    Journal of Computational Physics 258(1) (2014), pp. 509-523.
    Article - Preprint

Articles published in 2013

  • On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit
    Rémi Carles
    SIAM Journal on Numerical Analysis 51(6) (2013), pp. 3232-3258.
    Article (DOI, PDF) - Preprint

  • An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
    Christophe Besse, Rémi Carles, Florian Méhats
    Multiscale Modeling and Simulations 11(4) (2013), pp. 1228-1260.
    Article (DOI, PDF) - Preprint

  • Particle-Based Anisotropic Surface Meshing
    Zichun Zhong, Xiaohu Guo, Wenping Wang, Bruno Lévy, Feng Sun, Yang Liu and Weihua Mao
    ACM Transactions on Graphics - special issue ACM SIGGRAPH 2013 conference proceedings 32(4) (2013), Article No. 99.
    Article - Preprint

  • Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
    Xavier Antoine, Weizhu Bao, Christophe Besse
    Computer Physics Communications 184(12) (2013), pp. 2621-2633.
    Article - Preprint