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Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations

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Abstract

A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisymplectic conservation law, is presented to solve the Klein-Gordon-Schrödinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China

    LingHua Kong & Lan Wang

  2. School of Science, Beijing University of Chemical Technology, Beijing, 100029, China

    ShanShan Jiang

  3. School of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    YaLi Duan

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  1. LingHua Kong
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  2. Lan Wang
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  3. ShanShan Jiang
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  4. YaLi Duan
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Correspondence to LingHua Kong.

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Kong, L., Wang, L., Jiang, S. et al. Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations. Sci. China Math. 56, 915–932 (2013). https://doi.org/10.1007/s11425-013-4575-3

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  • DOI: https://doi.org/10.1007/s11425-013-4575-3

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