| 求解非线性方程的Jacobi椭圆展开法和F-展式法--以KdV方程为例 |
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| 引用本文： | 朱高生,周宇斌.求解非线性方程的Jacobi椭圆展开法和F-展式法--以KdV方程为例[J].吉林工学院学报,2006,27(1):56-59. |
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| 作者姓名： | 朱高生 周宇斌 |
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| 作者单位： | 天津大学理学院 天津300072(朱高生)，兰州大学数学与统计学院 甘肃兰州730000(周宇斌) |
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| 基金项目： | 国家自然科学基金资助项目(10571134) |
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| 摘 要： | 借助齐次平衡原则,构造一种新的精确解的方法F-展式法。F-展式法可看作最近提出的Jacobi椭圆函数法的推广,获得了KdV方程的多组新的Jacobi椭圆函数解,与其它结果比较,最大的进步是将解表示为两个函数的多项式形式。
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| 关 键 词： | 齐次平衡法 F-展式法 KdV方程 |
| 文章编号： | 1006-2939（2006）01-0056-04 |
| 收稿时间： | 2005-12-18 |
| 修稿时间： | 2005年12月18 |
Solve the nonlinear equation with Jacobi ellicptic function expansion and F-expansion methods illustrated by KdV quation |
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| ZHU Gao-sheng,ZHOU Yu-bin.Solve the nonlinear equation with Jacobi ellicptic function expansion and F-expansion methods illustrated by KdV quation[J].Journal of Jilin Institute of Technology,2006,27(1):56-59. |
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| Authors: | ZHU Gao-sheng ZHOU Yu-bin |
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| Institution: | 1. School of Science, Tianjin University, Tianjin 300072, China; 2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China |
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| Abstract: | By means of the homogeneous balance principle,F-expansion method,a rather new one to construct the precise solutions,is given here.It can be called as the extension of Jacobi elliptic(function method).We acquire several new groups of Jacobi elliptic function solutions for KdV(equation).Being compared with the results obtained by other methods,its greatest progress is that the solutions can be expressed by a polynomial of two functions. |
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| Keywords: | homogeneous balance principle F-expansion method KdV equation |
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