New High-Order Energy Preserving Method of the Fractional Coupled Nonlinear Schrodinger Equations

The symplectic structure is given for the fractional coupled nonlinear Schrodinger 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 Schrodinger 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.