| 非线性薛定谔方程的平均向量场方法 |
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| 引用本文： | 李昊辰,孙建强,骆思宇.非线性薛定谔方程的平均向量场方法[J].计算数学,2013,35(1):59-66. |
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| 作者姓名： | 李昊辰 孙建强 骆思宇 |
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| 作者单位： | 海南大学信息科学技术学院数学系, 海口 570228 |
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| 基金项目： | 国家自然科学基金项目(11161017);海南大学科研启动基金项目(kyqd1053);海南大学青年基金项目(qnjj1022)资助 |
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| 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.
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| 关 键 词： | AVF格式 保能量算法 非线性薛定谔方程 |
| 收稿时间： | 2012-06-25; |
AN AVERAGED VECTOR FIELD METHOD FOR THE NONLINEAR SCHRDINGER EQUATION |
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| Li Haochen
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Sun Jianqiang
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Luo Siyu.AN AVERAGED VECTOR FIELD METHOD FOR THE NONLINEAR SCHRDINGER EQUATION[J].Mathematica Numerica Sinica,2013,35(1):59-66. |
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| Authors: | Li Haochen Sun Jianqiang Luo Siyu |
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| Institution: | Institute of Information Science and Technology, Hainan University, Department of Mathematics, Haikou 570228, China |
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| Abstract: | The averaged vector field method (AVF) for the nonlinear Schrödinger equation which is a energy-preserving method theoretically is proposed. The nonlinear Schrödinger equation is simulated by the AVF method and the symplectic method respectively, and the energypreserving properties for the nonlinear Schrödinger equation of two methods are compared. Numerical results show that the AVF scheme can well simulate the soliton evolution behaviors of the nonlinear Schrödinger equation, and preserves the energy-preserving property better than the symplectic scheme. |
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| Keywords: | AVF method energy-preserving method nonlinear Schrö dinger equation |
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