Time splitting methods and the semi-classical limit for nonlinear Schrödinger equations

16 Jun 2016, 11:30
45m
Salle de Réunion - Bâtiment M2 ()

Salle de Réunion - Bâtiment M2

Speaker

Rémi Carles (Institut Montpelliérain Alexander Grothendieck)

Description

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.

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