中文摘要：

利用平均向量场方法（AVF）对非线性薛定谔方程进行求解，在理论上得到了一个保非线性薛定谔方程描述的系统能量守恒的AVF格式，再分别用非线性薛定谔方程的AVF格式和辛格式数值模拟孤立波的演化行为，并比较两个格式是否保系统能量守恒特性．数值结果表明，AVF格式也能很好地模拟孤立波的演化行为，并且比辛格式更能保持系统的能量守恒．

英文摘要：

The averaged vector field method （AVF） ior the nonlinear bchrodmger equation is a energy-preserving method theoretically is proposed. The nonlinear Schr6dinger equation is simulated by the AVF method and the symplectie method respectively, and the energy- preserving properties for the nonlinear Sehr6dinger equation of two methods are compared. Numerical results show that the AVF scheme can well simulate the soliton evolution behaviors of the nonlinear Schr6dinger equation, and preserves the energy-preserving property better than the symplectic scheme.