29 citations · 61 across the 17 of their papers we have counts for
22 papers
Computation of excited states for the nonlinear Schr{ö}dinger equation: numerical and theoretical analysis
Christophe Besse, Romain Duboscq, Stefan Le Coz
Our goal is to compute excited states for the nonlinear Schr{ö}dinger equation in the radial setting. We introduce a new technique based on the Nehari manifold approach and give a…
The logarithmic Bramson correction for Fisher-KPP equations on the lattice
Christophe Besse, Grégory Faye, Jean-Michel Roquejoffre +1
We establish in this paper the logarithmic Bramson correction for Fisher-KPP equations on the lattice . The level sets of solutions with step-like initial conditions ar…
Asymptotic behavior of nonlocal bistable reaction-diffusion equations
Christophe Besse, Alexandre Capel, Grégory Faye +1
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending o…
Spreading properties for SIR models on homogeneous trees
Christophe Besse, Grégory Faye
We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic…
Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library
Christophe Besse, Romain Duboscq, Stefan Le Coz
Nonlinear quantum graphs are metric graphs equipped with a nonlinear Schr{ö}dinger equation. Whereas in the last ten years they have known considerable developments on the theoreti…
Dynamics of epidemic spreading on connected graphs
Christophe Besse, Grégory Faye
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a sta…
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions
Guillaume Bertoli, Christophe Besse, Gilles Vilmart
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation…
Gradient Flow Approach to the Calculation of Stationary States on Nonlinear Quantum Graphs
Christophe Besse, Romain Duboscq, Stefan Le Coz
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the n…
Discrete transparent boundary conditions for the two-dimensional leap-frog scheme
Christophe Besse, Jean-François Coulombel, Pascal Noble
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equ…
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…
A conservation law with spatially localized sublinear damping
Christophe Besse, Rémi Carles, Sylvain Ervedoza
We consider a general conservation law on the circle, in the presence of a sublinear damping. If the damping acts on the whole circle, then the solution becomes identically zero in…
Restoring quasi-reversibility with a single topological charge
Juan Pablo Álvarez Zúñiga, Romain Duboscq, Christophe Besse +2
We numerically study a rotating Bose-Einstein condensate placed transiently over the critical rotation frequency i.e. in a regime where the rotation frequency is larger than the ra…
Discrete transparent boundary conditions for the mixed KDV-BBM equation
Christophe Besse, Pascal Noble, David Sanchez
In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) Benjamin-Bona-Mahoney (BBM) equation which models water waves in the smal…
Domain decomposition algorithms for the two dimensional nonlinear Schr{ö}dinger equation and simulation of Bose-Einstein condensates
Christophe Besse, Feng Xing
In this paper, we apply the optimized Schwarz method to the two dimensional nonlinear Schr{ö}dinger equation and extend this method to the simulation of Bose-Einstein condensates (…
Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation
Christophe Besse, Matthias Ehrhardt, Ingrid Lacroix-Violet
In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artific…
High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates
Christophe Besse, Guillaume Dujardin, Ingrid Lacroix-Violet
This article deals with the numerical integration in time of nonlinear Schrödinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates…
Domain decomposition algorithms for two dimensional linear Schrödinger equation
Christophe Besse, Feng Xing
This paper deals with two domain decomposition methods for two dimensional linear Schr{ö}dinger equation, the Schwarz waveform relaxation method and the domain decomposition in spa…
Schwarz waveform relaxation method for one dimensional Schr{ö}dinger equation with general potential
C Besse, F Xing
In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{ö}dinger equation with a general linear or a nonlinear potential. We propose a new…
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…
An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
Christophe Besse, Rémi Carles, Florian Méhats
We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulatio…
Transparent boundary conditions for locally perturbed infinite hexagonal periodic media
Christophe Besse, Julien Coatleven, Sonia Fliss +2
In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorizat…
Monotonicity properties of blow-up time for nonlinear Schrödinger equation: numerical tests
Christophe Besse, Rémi Carles, Norbert Mauser +1
We consider the focusing nonlinear Schrödinger equation, in the -critical and supercritical cases. We investigate numerically the dependence of the blow-up time on a parameter…