| KdV方程的多辛Fourier拟谱格式及其孤立波解的数值模拟 |
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| 引用本文： | 宋松和,陈亚铭,朱华君.KdV方程的多辛Fourier拟谱格式及其孤立波解的数值模拟[J].安徽大学学报(自然科学版),2010,34(4). |
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| 作者姓名： | 宋松和 陈亚铭 朱华君 |
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| 作者单位： | 国防科技大学,数学与系统科学系,湖南,长沙,410073 |
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| 基金项目： | 国家自然科学基金资助项目，国家"973"重大基础研究基金资助项目 |
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| 摘 要： | 基于其多辛方程组的形式,对满足周期边界条件的KdV方程,在空间方向用Fourier拟谱方法、时间方向用中点隐式辛格式进行离散,得到了KdV方程的多辛Fourier拟谱格式及其相应的守恒律.对不同的孤立波解进行数值模拟,结果验证了所构造格式的有效性与长期数值稳定性.
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| 关 键 词： | KdV方程 Fourier拟谱格式 孤立波 多辛 |
Multi-symplectic Fourier pseudospectral scheme and simulation of soliton solutions for the KdV equation |
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| SONG Song-he,CHEN Ya-ming,ZHU Hua-jun.Multi-symplectic Fourier pseudospectral scheme and simulation of soliton solutions for the KdV equation[J].Journal of Anhui University(Natural Sciences),2010,34(4). |
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| Authors: | SONG Song-he CHEN Ya-ming ZHU Hua-jun |
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| Institution: | SONG Song-he,CHEN Ya-ming,ZHU Hua-jun(Department of Mathematics and System Science,National University of Defense Technology,Changsha 410073,China) |
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| Abstract: | The KdV equation with periodic boundary condition was considered in this paper.Based on its multi-symplectic formulation,a multi-symplectic Fourier pseudospectral scheme for the KdV equation was constructed by using Fourier pseudospectral method in space direction and midpoint implicit symplectic scheme in time direction.Its discrete multi-symplectic conservation law was also obtained.The simulation of different solitons showed that the scheme constructed in this paper was effective and had excellent long t... |
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| Keywords: | KdV equation Fourier pseudospectral scheme soliton multi-symplectic |
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