A fourth-order energy preserving composition scheme for multi-symplectic structure partial differential equations have been proposed. The accuracy and energy conservation properties of the new scheme were verified. The new scheme is applied to solve the multi-symplectic sine-Gordon equation with periodic boundary conditions and compared with the corresponding second-order average vector field scheme and the second-order Preissmann scheme. The numerical experiments show that the new scheme has fourth-order accuracy and can preserve the energy conservation properties well.

The symplectic structure is given for the fractional coupled nonlinear Schrödinger equations. The Fourier spectral method and the fourth-order combination average vector field (AVF) method are applied to discretize the structure, and a new format for the fractional coupled nonlinear Schrödinger equations is obtained. The numerical experiments are showed to illustrate the property of the new format. The new scheme can maintain the energy conservation property better than the classical symplectic scheme.