High order energy-preserving method for the space fractional Klein–Gordon-Zakharov equations

The space fractional Klein–Gordon-Zakharov equations are transformed into the multi-symplectic structure system by introducing new auxiliary variables. The multi-symplectic system, which satisfies the multi-symplectic conservation, local energy and momentum conservation, is discretizated into the semi-discrete multi-symplectic system by the Fourier pseudo-spectral method. The second order multi-symplectic average vector field method is applied to the semi-discrete system. The fully discrete energy preserving scheme of the space fractional Klein–Gordon-Zakharov equation is obtained. Based on the composition method, a fourth order energy preserving scheme of the Riesz space fractional Klein–Gordon-Zakharov equations is also obtained. Numerical experiments confirm that these new schemes can have computing ability for a long time and can well preserve the discrete energy conservation property of the equations.