三耦合薛定谔方程组的离散线积分方法  

Discrete line integral method for 3-coupled Schr?dinger equations

作　　者：王一帆[1] 孙建强[1] 陈宵玮 Wang Yifan;Sun Jianqiang;Chen Xiaowei(College of Information Science and Technology,Hainan University,Haikou 570228.China)

机构地区：[1]海南大学信息科学技术学院,海口570228

出　　处：《河南师范大学学报（自然科学版）》2018年第5期20-25,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11561018);海南省自然科学基金(114003)

摘　　要：三耦合薛定谔方程组具有能量守恒特性,用保能量算法数值模拟三耦合薛定谔方程组孤立波的演化行为具有重要意义.将三耦合薛定谔方程组转化成典则哈密尔顿系统,利用Boole离散线积分方法进行数值求解,得到三耦合薛定谔方程的一个新的保能量格式.利用新格式数值模拟方程组在不同参数下孤立波的行为.数值结果表明离散线积分方法可以很好模拟方程组孤立波的行为和保方程的能量守恒.Three coupled Schrodinger equations have the energy conservation property.Energy conservation numerical method of three coupled Schrodinger equations has important meaning in simulating the solitary wave behaviors of the equatoions.In this paper,three coupled Schrodinger equations were transformed into the classical Hamilton system,the Boole discrete line integral method was applied to the classical Hamilton system.The new energy conserving schemes of three coupled Schrodinger equations is obtained.The new scheme is applied to simulate the solitary wave behaviors with different parameters.The numerical results show that the discrete line integral method can well simulate the solitary wave behaviors of the equations and preserve the energy conservation.

关 键 词：三耦合薛定谔方程组 哈密尔顿系统 离散线积分方法 谱方法 

分 类 号：O241.5[理学—计算数学]