Preprints
Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation, with
Quentin Chauleur, Radu Chicireanu, Jean-Claude Garreau and Adam Rançon,
(submitted, April 2024)
Uniform estimates for a fully discrete scheme integrating the linear heat equation on a bounded interval with pure Neumann boundary conditions, with
Pauline Lafitte,
(submitted, November 2023)
Articles
A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates (preprint), with
I. Lacoix-Violet
and A. Nahas,
Mathematics and Computers in Simulation, vol. 229, 409-434, 2025
High order linearly implicit methods for semilinear evolution PDEs (preprint), with
I. Lacroix-Violet,
The SMAI Journal of computational mathematics, vol. 10, 325-354, 2024
Â- and Î-stability of collocation Runge-Kutta methods (preprint), with
Ingrid Lacroix-Violet,
Applied Numerical Mathematics, vol. 202, 158-172, 2024
Numerical computation of dark solitons of a nonlinear nonlocal Schrödinger equation (preprint), with
André de Laire and Salvador López-Martínez,
Journal of Nonlinear Science, vol. 34, no. 23, 2024
Modulational instability in randomly dispersion-managed fiber links (preprint), with A. Armaroli, M. Conforti, A. Kudlinski, A. Mussot and S. De Bievre,
Physical Review A, vol. 108, no. 2, 2023
Exponential integrators for the stochastic Manakov equation (preprint), with
A. Berg
and D. Cohen,
Journal of Computational Dynamics, vol. 10, no. 2, 323-344, 2023
High order linearly implicit methods for evolution equations
(article in HAL), with
I. Lacroix-Violet,
ESAIM: M2AN, vol. 56, no. 3, 2022
Stochastic modulational instability in the nonlinear Schrödinger equation
with colored random dispersion
(preprint), with
A. Armaroli,
A. Kudlinski,
A. Mussot,
S. Trillo,
S. De Bièvre, and
M. Conforti,
Physical Review A, vol. 105, No. 1, 2022
Lie-Trotter splitting for the nonlinear stochastic Manakov system (preprint), with
A. Berg
and D. Cohen,
Journal of Scientific Computing, vol. 88, 2021
Modulational instability in optical fibers with randomly-kicked normal dispersion (preprint), with A. Armaroli, S. Rota-Norati, A. Mussot, A. Kudlinski, S. Trillo, M. Conforti and S. De Bièvre,
Physical Review A, vol. 103, issue 5, 2021
Energy preserving methods for nonlinear Schrödinger equations
(preprint), with
C. Besse, S. Descombes, and I. Lacroix-Violet,
IMA Journal of Numerical Analysis, vol. 41, issue 1, 618–653, 2021
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations (preprint), with
F. Hérau and P. Lafitte,
Numerische Mathematik, vol. 144, 615–697, 2020
Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
(preprint), with
D. Cohen,
Stochastics and Partial Differential Equations: Analysis and Computations, vol. 5, no. 4, 592-613, 2017
Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger
equations
(preprint), with
C.G.L. Thiofack, S. Coulibaly,
M. Taki and S. De Bièvre,
Physics Letters A, vol.381, no. 24, 1999-2003, 2017
High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates
(preprint), with
C. Besse and I. Lacroix-Violet,
SIAM Journal on Numerical Analysis, vol. 55, no. 3, 1387-1411, 2017
Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation
(preprint), with
M. Conforti,
A. Mussot,
A. Kudlinski,
S. Rota Nodari,
S. De Bièvre,
A. Armaroli, and
S. Trillo,
Physical Review Letters, vol. 117, no. 1, 013901, 2016
Asymptotic
behavior of splitting schemes involving time-subcycling techniques (preprint), with
P. Lafitte,
IMA Journal of Numerical Analysis, vol. 36, no. 4, 1804-1841, 2016
Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schrödinger equations (preprint), with
C.G.L. Thiofack, S. Coulibaly,
M.
Taki and S. De Bièvre,
Physical Review A, vol. 92, no. 4, 043837, 2015
Modulational instability in dispersion-kicked optical fibers (preprint), with
S. Rota Nodari, M. Conforti, A. Kudlinski, A. Mussot, S. Trillo, and S. De Bièvre,
Physical Review A, vol. 92, no. 1, 013810, 2015
Excitation of radial
collective modes in a quantum dot: Beyond linear response (preprint), with
Viðar Guðmundsson,
Sigtryggur Hauksson, Arni Johnsen, Gilbert Reinisch, Andrei Manolescu
and Christophe Besse,
Annalen der Physik, vol. 526, no. 5-6, 235–248, 2014
Energy-preserving integrators for stochastic Poisson systems (preprint),
with
D. Cohen,
Communications in Mathematical Sciences, vol. 12, no. 8, 1523-1539, 2014
Asymptotics of linear initial boundary value
problems with periodic boundary data on the half-line and finite
intervals (preprint),
Proceedings of the Royal Society A, vol. 465, no. 2111, 3341-3360, 2009
Propagation of Gevrey regularity over
long times for the fully discrete Lie Trotter splitting scheme applied to the
linear Schrödinger equation (preprint),
with
F. Castella,
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 43, no. 4, 651-676, 2009
Exponential Runge-Kutta methods for the Schrödinger equation (preprint),
Applied Numerical Mathematics, vol 59, no. 8, 1839-1857, 2009
Moments analysis in homogeneous Markov reward models (preprint),
with F.
Castella and B.
Sericola,
Methodology and Computing in Applied Probability, vol. 11, no. 4, 583-601, 2008
Normal
form and long time analysis of splitting schemes for the linear Schrödinger
equation with small potential
(preprint), with
E. Faou,
Numerische Mathematik, vol. 108, no. 2, 223-262, 2007
Conference proceedings
Modulation instability in periodically dispersion kicked optical fibers, with M. Conforti, S. Rota Nodari, A. Kudlinski, A. Mussot, S. Trillo, and S. De Bievre,
2015 European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference, Optical Society of America
Notes
"Long time behavior of splitting methods
applied to the linear Schrödinger equation", with
E. Faou,
C.R. Acad. Sci. Paris, Sér. I, 344, 89-92, 2007
Reports
"Sobolev estimates for splitting schemes applied to the linear Schrödinger equation", with
E. Faou,
Mathematisches Forschungsinstitut Oberwolfach Report No. 14/2006
Thesis
"Etude de
schémas de discrétisation en temps de l'équation de Schrödinger"
(English & French)
Defended on June 13th 2008,
University of Rennes I, IRMAR and INRIA Rennes Bretagne Atlantique
Habilitation à diriger des recherches
"Contribution à l'analyse numérique de problèmes d'évolution : comportements asymptotiques et applications à l'équation de
Schrödinger"
(English & French)
Defended on November 12th 2018,
University of Lille, Inria