5 papers · 1 filter
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…
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 bou…