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Structure-preserving Gauss methods for the nonlinear Schrödinger equation

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Abstract

We use the scalar auxiliary variable (SAV) reformulation of the nonlinear Schrödinger (NLS) equation to construct structure-preserving SAV–Gauss methods for the NLS equation, namely \(L^2\)-conservative methods satisfying a discrete analogue of the energy (the Hamiltonian) conservation of the equation. This is in contrast to Gauss methods for the standard form of the NLS equation that are \(L^2\)-conservative but not energy-conservative. We also discuss efficient linearizations of the new methods and their conservation properties.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Ioannina, 451 10, Ioannina, Greece

    Georgios Akrivis

  2. Institute of Applied and Computational Mathematics, FORTH, 700 13, Heraklion, Crete, Greece

    Georgios Akrivis

  3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Dongfang Li

  4. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Dongfang Li

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  1. Georgios Akrivis
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  2. Dongfang Li
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Correspondence to Georgios Akrivis.

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The work of Dongfang Li was partially supported by NSFC (no. 11771162 and no. 11971010).

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Akrivis, G., Li, D. Structure-preserving Gauss methods for the nonlinear Schrödinger equation. Calcolo 58, 17 (2021). https://doi.org/10.1007/s10092-021-00405-w

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