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

Yifei Huang, Gang Peng, Gengen Zhang and Hong Zhang

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 603-618

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.

Keywords: Schrödinger–KdV equations; Structure-preserving method; Runge–Kutta method; Fourier pseudo-spectral method (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:603-618

DOI: 10.1016/j.matcom.2023.01.031

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