Rémi Carles (Institut Montpelliérain Alexander Grothendieck)
We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrödinger equation, in the semi-classical limit, with initial data under the form of WKB states. Both the exact and the numerical solutions keep a WKB structure, on a time interval independent of the Planck constant. We prove error estimates, which show that the quadratic observables can be computed with a time step independent of the Planck constant. We give a flavor of the functional framework, based on time-dependent analytic spaces.