Semi-explicit symplectic partitioned Runge–Kutta Fourier pseudo-spectral scheme for Klein–Gordon–Schrödinger equations

Abstract

In the manuscript, we propose an explicit symplectic partitioned Runge–Kutta Fourier pseudo-spectral (SPRK-FPS) scheme for the coupled Klein–Gordon–Schrödinger (KGS) equation. It is explicit in term of iteration since it is only required to solve two linear algebraic equations at each marching time step. Furthermore, it does not only symplectic geometric structure-preserving, but also charge-preserving and energy-preserving. The numerical results are in good agreement with the theoretical analysis.