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| 高阶广义KDV方程和KP方程的数值解法 | |
| 引用本文： | 张天德,鲁统超,左进明,曹庆杰.高阶广义KDV方程和KP方程的数值解法[J].系统科学与数学,2005,25(6):658-668. |
| 作者姓名： | 张天德 鲁统超 左进明 曹庆杰 |
| 作者单位： | 1. 山东大学数学与系统科学学院,济南,250100 2. 山东理工大学数学与信息科学学院,淄博,255049 3. 山东大学数学与系统科学学院,济南,250100;阿伯丁大学工程系,阿伯丁,Ab24,302,英国 |
| 基金项目： | 国家自然科学基金(10471079) 教育部高等学校博士点基金(20030422049)资助课题． |
| 摘 要： | 采用一种线性隐格式来解3-阶和5-阶的广义Korteweg-De Vries(KDV)方程,对这种方法做一推广,就能应用到它的二维形式广义Kadomtsew-Petviashvili(KP)方程．这种方法是无条件稳定的,且是无损耗的．数值实验描述了一个线性孤波运动的情形以及两个孤波交互的情形,从结果来看,它们满足孤立子解的两个守恒-动量守恒和能量守恒． |
| 关 键 词： | 数值解法 KDV／KP方程 孤波 稳定性分析 相位差 |
| 修稿时间： | 2003年12月30 |
COMPUTATIONAL METHODS FOR HIGH-LEVEL GENERALIZED KDV EQUATION AND KP EQUATION |
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| Zhang Tiande,Lu Tongchao,Zuo Jinming,Cao Qingjie.COMPUTATIONAL METHODS FOR HIGH-LEVEL GENERALIZED KDV EQUATION AND KP EQUATION[J].Journal of Systems Science and Mathematical Sciences,2005,25(6):658-668. | |
| Authors: | Zhang Tiande Lu Tongchao Zuo Jinming Cao Qingjie |
| Institution: | (1)School of Mathematics and Systems Science, Shandong Univ, Jinan 250100;(2) Department of Mathematics, Shandong University of Technology, Zibo 255049;(3)School of Mathematics and Systems Science, Shandong University, Jinan 250100;Department of Engineering, The University of Ab |
| Abstract: | Computational methods based on a linearized implicit scheme are proposed for generalized Korteweg-de Vries(KDV) equation. The methods are applied with minor modifications to the generalized Kadomtsew-Petviashvili(KP) equation. An important advantage gained from the linearized implicit methods is unconditional stability. Numerical results portraying a single-line-soliton solution and the interaction of two-line solition are reported for the 5-order KDV and 6-order KP equations. |
| Keywords: | Computational methods KDV/KP equation solitary waves stability analysis phase error |
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