1 citations · 2 across the 14 of their papers we have counts for
16 papers
Dependence of the nonlinear Schr{ö}dinger flow upon the nonlinearity
Rémi Carles, Quentin Chauleur, Guillaume Ferriere
We consider the defocusing nonlinear Schr{ö}dinger equation in the energy-subcritical case, and investigate the dependence of the solution upon the power of the nonlinearity. Speci…
Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
Quentin Chauleur, Gaspard Kemlin
We prove the convergence in Zhidkov spaces of the first-order Lie-Trotter and the second-order Strang splitting schemes for the time integration of the Gross-Pitaesvkii equation wi…
On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers
Rémi Carles, Quentin Chauleur, Guillaume Ferriere +1
We consider the ground states of the nonlinear Schr{ö}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate the…
On the dependence of the nonlinear Schrodinger flow upon the power of the nonlinearity
Rémi Carles, Quentin Chauleur, Guillaume Ferriere
We prove continuity properties for the flow map associated to the defocusing energy-subcritical power-like nonlinear Schr{ö}dinger equation, when the power varies. We show local in…
High order uniform in time schemes for weakly nonlinear Schrödinger equation and wave turbulence
Quentin Chauleur, Antoine Mouzard
We introduce two multiscale numerical schemes for the time integration of weakly nonlinear Schrödinger equations, built upon the discretization of Picard iterates of the solution.…
On the propagation of high regularity for the logarithmic Schr{ö}dinger equation
Quentin Chauleur, Guillaume Ferriere
We investigate both the instantaneous loss and the persistence of high regularity for the one-dimensional logarithmic Schr{ö}dinger equation in symmetric domains under various boun…
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…
Continuum limit of the discrete nonlinear Klein-Gordon equation
Quentin Chauleur
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of…
Finite volumes for the Gross-Pitaevskii equation
Quentin Chauleur
We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux app…
The logarithmic Schr{ö}dinger equation with spatial white noise on the full space
Quentin Chauleur, Antoine Mouzard
We solve the Schr{ö}dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d 2. Because of the nonlinearity, the regularity structur…
Growth of Sobolev norms and strong convergence for the discrete nonlinear Schr{ö}dinger equation
Quentin Chauleur
We show the strong convergence in arbitrary Sobolev norms of solutions of the discrete nonlinear Schr{ö}dinger on an infinite lattice towards those of the nonlinear Schr{ö}dinger e…
Discrete quantum harmonic oscillator and Kravchuk transform
Quentin Chauleur, Erwan Faou
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from…
Around plane waves solutions of the Schr{ö}dinger-Langevin equation
Quentin Chauleur, Erwan Faou
We consider the logarithmic Schr{ö}dinger equations with damping, also called Schr{ö}dinger-Langevin equation. On a periodic domain, this equation possesses plane wave solutions th…
The isothermal limit for the compressible Euler equations with damping
Quentin Chauleur
We consider the isothermal Euler system with damping. We rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit $\righ…
Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equation
Quentin Chauleur
We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Kortew…
Dynamics of the Schr{ö}dinger-Langevin Equation
Quentin Chauleur
We consider the nonlinear Schr{ö}dinger-Langevin equation for both signs of the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian solutions for large times,…