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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…