High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime
Year: 2026
Type: preprint
Abstract: Nonlinear coupled dispersive models arise in numerous physical settings, including quantum electrodynamics, nonlinear optics, and plasma dynamics. In the nonrelativistic limit, such systems exhibit rapid temporal oscillations of wavelength $\mathcal{O}(\varepsilon^{2})$, controlled by a dimensionless parameter $0<\varepsilon\ll 1$. Moreover, owing to the Yukawa-coupled interaction terms, numerical schemes that simultaneously achieve high-order uniform accuracy and approximately preserve the mass and the energy are essential for reliable simulations. In this work, we propose a class of fully discrete schemes for nonlinear coupled dispersive models in the nonrelativistic regime that achieve higher-order uniform accuracy and approximately preserve both invariants over long times. Spatial discretization is based on the Fourier pseudospectral method, and time advancement employs two-scale exponential Runge-Kutta methods. Numerical experiments on the highly oscillatory Klein-Gordon-Dirac and Klein-Gordon-Schrödinger equations in one, two, and three dimensions confirm that the resulting schemes attain the theoretically predicted uniform accuracy and the long-time near-conservation of both invariants.
Source: arXiv (Cornell University)
Authors: Wang, Lina, Li, Jiyong, Wang, Bin
Institutions: Xi'an Jiaotong University, Hebei Normal University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2217401733, G6310457247
OpenAlex ID: W7221819464