90 citations · 370 across the 42 of their papers we have counts for
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Resonant time steps and instabilities in the numerical integration of Schrödinger equations
Erwan Faou, Tiphaine Jézéquel
We consider the linear and non linear cubic Schrödinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of…
The weakly nonlinear large box limit of the 2D cubic nonlinear Schrödinger equation
Erwan Faou, Pierre Germain, Zaher Hani
We consider the cubic nonlinear Schrödinger (NLS) equation set on a two dimensional box of size with periodic boundary conditions. By taking the large box limit …
Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation
Erwan Faou, Ludwig Gauckler, Christian Lubich
Plane wave solutions to the cubic nonlinear Schrödinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data tha…
Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme
Charles-Edouard Bréhier, Erwan Faou
We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We s…