Abstract: Constructing the high order energy preserving scheme for the Ito-type coupled KdV equation with the energy conservation property has the important application in simulating the motion of the equation. In this paper, the high order energy preserving scheme for the Ito-type coupled KdV equation is obtained by applying the fourth order average vector field method and the Fourier pseudo spectral method. The new high order energy preserving scheme is applied to simulate the solitary wave behaviors  of the equation. Numerical results show the new high order energy preserving scheme can well simulate the solitary wave evolution behaviors of the Ito-type coupled KdV equation and preserve the discrete energy conservation exactly.

Key words: average vector field method, high order energy-preserving method, the solitary wave, the Ito-type coupled KdV equation