High-order energy-preserving schemes for the Klein-Gordon-Zakharov system

This work presents a family of highly accurate energy-conserving algorithms for solving the Klein-Gordon-Zakharov equation, developed through the quadratic auxiliary variable (QAV) transformation approach. The proposed methodology employs Fourier pseudospectral discretization for spatial dimensions and symplectic Runge-Kutta methods for temporal integration, ensuring exact energy conservation in the fully-discrete framework. To handle the resulting nonlinear equations, we construct an efficient fixed-point iteration algorithm. Extensive numerical experiments are performed, comparing the proposed method with existing schemes, and the results show excellent consistency with theoretical expectations.