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

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Abstract

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. 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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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, CNRS & Univ. Montpellier, CC51, Place E. Bataillon, 34095, Montpellier, France

    Rémi Carles & Clément Gallo

Authors
  1. Rémi Carles
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  2. Clément Gallo
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Correspondence to Rémi Carles.

Additional information

This work was supported by the French ANR projects SchEq (ANR-12-JS01-0005-01) and BECASIM (ANR-12-MONU-0007-04).

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Carles, R., Gallo, C. On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity. Numer. Math. 136, 315–342 (2017). https://doi.org/10.1007/s00211-016-0841-y

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  • DOI: https://doi.org/10.1007/s00211-016-0841-y

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