| 应用F展开法求KdV方程的周期波解 |
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| 引用本文： | 李向正,王明亮,李晓燕.应用F展开法求KdV方程的周期波解[J].应用数学,2005,18(2):303-307. |
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| 作者姓名： | 李向正 王明亮 李晓燕 |
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| 作者单位： | 1. 河南科技大学数理系,河南,洛阳,471003
2. 河南科技大学数理系,河南,洛阳,471003;兰州大学数学系,兰州,730000 |
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| 基金项目： | 国家自然科学基金，国家自然科学基金，the Science Foundation of Henan University of Science and Technology |
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| 摘 要： | 提出了求非线性数学物理演化方程周期波解的F展开法,该方法可看作最近提出的扩展的Jacobi椭圆函数展开方法的浓缩.直接利用F展开法而不计算Jacobi椭圆函数,我们可同时得到著名的KdV方程的多个用Jacobi椭圆函数表示的周期波解.当模数m→1 时,可得到双曲函数解(包括孤立波解).
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| 关 键 词： | F展开法 KdV方程 周期波解 Jacobi椭圆函数 孤立波解 |
Applications of F-expansion to Periodic Wave Solutions for KdV Equation |
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| LI Xiang-zheng,WANG Ming-liang,LI Xiao-yan.Applications of F-expansion to Periodic Wave Solutions for KdV Equation[J].Mathematica Applicata,2005,18(2):303-307. |
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| Authors: | LI Xiang-zheng WANG Ming-liang LI Xiao-yan |
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| Abstract: | We present a F-expansion method for fi nd ing periodic wave solutions of nonlinear evolution equations in mathematical phy sics,which can be thought of as a concentration of extended Jacobi elliptic func tion expansion method proposed more recently.By using the F-expansion,witho ut calculating Jacobi elliptic functions,we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the famous KdV equation.When the modulus m approaches to 1,the hyperbolic function solutio ns (including the solitary wave solutions) are also given. |
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| Keywords: | F-expansion KdV equation Periodic wave solutions J acobi elliptic functions Solitary wave solutions |
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