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High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations

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  • Huang, Yifei
  • Peng, Gang
  • Zhang, Gengen
  • Zhang, Hong

Abstract

A novel class of high-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations is proposed and analyzed. With the aid of the quadratic auxiliary variable, an equivalent system is obtained from the original problem. The Fourier pseudo-spectral method is employed in spatial discretization and the symplectic Runge–Kutta method is utilized for the resulting semi-discrete system to arrive at a high-order fully discrete scheme. Simultaneously, the conservation of the original multiple invariants for the schemes are rigorously proven. Numerical experiments are performed to verify the theoretical analysis.

Suggested Citation

  • Huang, Yifei & Peng, Gang & Zhang, Gengen & Zhang, Hong, 2023. "High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 603-618.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:603-618
    DOI: 10.1016/j.matcom.2023.01.031
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    References listed on IDEAS

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    1. Barletti, L. & Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2018. "Energy-conserving methods for the nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 3-18.
    2. Ömer Oruç & Alaattin Esen & Fatih Bulut, 2016. "A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-16, September.
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