High order energy invariant fast algorithm for space two dimensional Klein-Gordon-Zakharov equations

Space two dimensional Klein-Gordon-Zakharov equations are directly changed into the Hamiltonian system with infinite dimensional space by the variational formula, which can be discretized into finite dimensional Hamiltonian system by Fourier pseudo-spectral method. The average vector field formulas with second and fourth order accuracy in time are utilized to compute the finite dimensional Hamiltonian system. In order to improve computation velocity of these formulas, the fast computation algorithm of these formulas is proposed by decomposing the spectral matrix. Solitary wave evolution of the equations is analyzed with different initial conditions by these new computational formulas. Energy invariant property, accuracy and computation efficiently of these new formulas are also investigated.