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A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions

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Abstract

The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and \(\mathcal{J}\) nondispersive fields \(\{n_j\}_{j=1}^\mathcal{J}\) with a propagating speed of \(1/\in_j\). In this paper, we extend our one-dimensional time-splitting spectral method (TSSP) for the generalized ZS into higher dimension. A main new idea is to reformulate the multi-dimensional wave equations for the nondispersive fields into a first-order system using a change of variable defined in the Fourier space. The proposed scheme TSSP is unconditionally stable, second-order in time and spectrally accurate in space. Moreover, in the subsonic regime, it allows numerical capturing of the subsonic limit without resolving the small parameters \(\in_j\). Numerical examples confirm these properties of this method

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Shi Jin

  2. Department of Mathematical Science, Tsinghua University, Beijing, 100084, P.R. China

    Shi Jin & Chunxiong Zheng

Authors
  1. Shi Jin
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  2. Chunxiong Zheng
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Correspondence to Shi Jin.

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Jin, S., Zheng, C. A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions. J Sci Comput 26, 127–149 (2006). https://doi.org/10.1007/s10915-005-4929-2

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  • DOI: https://doi.org/10.1007/s10915-005-4929-2

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