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Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times

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Abstract

Conservation properties of a full discretization via a spectral semi-discretization in space and a Lie–Trotter splitting in time for cubic Schrödinger equations with small initial data (or small nonlinearity) are studied. The approximate conservation of the actions of the linear Schrödinger equation, energy, and momentum over long times is shown using modulated Fourier expansions. The results are valid in arbitrary spatial dimension.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany

    Ludwig Gauckler & Christian Lubich

Authors
  1. Ludwig Gauckler
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  2. Christian Lubich
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Correspondence to Ludwig Gauckler.

Additional information

Communicated by Arieh Iserles.

Dedicated to Ernst Hairer on the occasion of his sixtieth birthday.

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Gauckler, L., Lubich, C. Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times. Found Comput Math 10, 275–302 (2010). https://doi.org/10.1007/s10208-010-9063-3

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  • DOI: https://doi.org/10.1007/s10208-010-9063-3

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