7 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. Spec…
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 th…
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 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 i…
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…
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.…