High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime

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 dimensionles