On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity

Rémi Carles; Clément Gallo

doi:10.1007/s00211-016-0841-y

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arXiv · 1602.03129

On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity

Rémi Carles·Clément Gallo

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Abstract

We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that 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. The functional framework is based on time-dependent analytic spaces, in order to overcome a previously encountered loss of regularity phenomenon.

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Rémi Carles, Clément Gallo. 2016-02-09. On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity. https://doi.org/10.1007/s00211-016-0841-y

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