38 citations · 99 across the 16 of their papers we have counts for
19 papers
Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation
Quentin Chauleur, Radu Chicireanu, Guillaume Dujardin +2
We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the n…
Uniform estimates for a fully discrete scheme integrating the linear heat equation on a bounded interval with pure Neumann boundary conditions
Guillaume Dujardin, Pauline Lafitte
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it pr…
Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation
André de Laire, Guillaume Dujardin, Salvador López-Martínez
The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been es…
Â-and Î-stability of collocation Runge-Kutta methods
Guillaume Dujardin, Ingrid Lacroix-Violet
This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for…
High order linearly implicit methods for semilinear evolution PDEs
Guillaume Dujardin, Ingrid Lacroix-Violet
This paper considers the numerical integration of semilinear evolution PDEs using the high order linearly implicit methods developped in a previous paper in the ODE setting. These…
Modulational instability in randomly dispersion-managed fiber links
Andrea Armaroli, Guillaume Dujardin, Alexandre Kudlinski +3
We study modulational instability in a dispersion-managed system where the sign of the group-velocity dispersion is changed at uniformly distributed random distances around a refer…
A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates
Guillaume Dujardin, Ingrid Lacroix-Violet, Anthony Nahas
This article introduces a new numerical method for the minimization under constraints of a discrete energy modeling multicomponents rotating Bose-Einstein condensates in the regime…
Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion
Andrea Armaroli, Guillaume Dujardin, Alexandre Kudlinski +4
We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort t…
Modulational instability in optical fibers with randomly-kicked normal dispersion
G. Dujardin, A. Armaroli, S. Rota Nodari +5
We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are eit…
Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
André Berg, David Cohen, Guillaume Dujardin
This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefr…
Exponential integrators for the stochastic Manakov equation
André Berg, David Cohen, Guillaume Dujardin
This article presents and analyses an exponential integrator for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optica…
High order linearly implicit methods for evolution equations
Guillaume Dujardin, Ingrid Lacroix-Violet
This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs. The systematic design of these method…
Energy preserving methods for nonlinear Schrödinger equations
Christophe Besse, Stephane Descombes, Guillaume Dujardin +1
This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it. The Cran…
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations
Guillaume Dujardin, Frédéric Hérau, Pauline Lafitte
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations o…
Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation
M. Conforti, A. Mussot, A. Kudlinski +5
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schrödinger equation can be accurately described by com…
Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{ö}dinger equations
Gaston Thiofack, Saliya Coulibaly, Majid Taki +2
It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{ö}dinger equation can drastically impact the spatial shape of the Peregrine soliton…
Modulational instability in dispersion-kicked optical fibers
S. Rota Nodari, M. Conforti, G. Dujardin +4
We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb…
Asymptotic behavior of splitting schemes involving time-subcycling techniques
Guillaume Dujardin, Pauline Lafitte
This paper deals with the numerical integration of well-posed multiscale systems of ODEs or evolutionary PDEs. As these systems appear naturally in engineering problems, time-subcy…
Excitation of radial collective modes in a quantum dot: Beyond linear response
Vidar Gudmundsson, Sigtryggur Hauksson, Arni Johnsen +4
We compare the response of five different models of two interacting electrons in a quantum dot to an external short lived radial excitation that is strong enough to excite the syst…