High-order energy-preserving exponential integrators for the Klein–Gordon–Zakharov equations

In this paper, we develop a novel high-order exponential integrator for solving the Klein–Gordon–Zakharov equations, which satisfies a discrete analogue of the energy conservation law. The key ingredient of our method is to first reformulate the original system as an exponential supplementary variable system based on the idea of the exponential supplementary variable method, and then discretize the reformulated system using the Fourier pseudo-spectral method in space and a high-order prediction–correction Lawson Runge–Kutta method in time. The proposed method is energy-preserving in the discrete setting, and it only requires solving several linear equations with constant coefficients plus a nonlinear algebraic system, which can be efficiently computed by the Newton iteration method per time step. Finally, we conduct a comprehensive numerical comparison between the newly developed method and the existing high-order energy-preserving methods.