中文摘要：

能量守恒格式对于准确地模拟微分方程的运动具有重要的意义。本文应用平均离散梯度法和辛算法求解耦合非线性薛定谔方程。数值结果表明平均离散梯度法能很好地模拟耦合非线性薛定谔方程在不同参数下孤立波的演化行为，并能精确地保持方程的离散能量。平均离散梯度法比相应的辛格式更好地保持方程的能量守恒。

英文摘要：

Energy preserving scheme is very important in simulating the behaviors of the d-ifferential equations. In this paper, we apply the average discrete gradient method and the symplectic method to solve the coupled nonlinear Schr＆#168;odinger equations. Numerical results show that the average discrete gradient method is able to simulate the solitary wave behaviors with different parameters very well, and also preserve the discrete energy of the coupled non-linear Schr＆#168;odinger equations exactly. The average discrete gradient method is better than the corresponding symplectic scheme in preserving the energy of the differential equation.