| 非线性波方程周期解的新方法 |
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| 引用本文： | 钱天虹,刘中飞,韩家骅. 非线性波方程周期解的新方法[J]. 安徽大学学报(自然科学版), 2006, 30(1): 58-62 |
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| 作者姓名： | 钱天虹 刘中飞 韩家骅 |
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| 作者单位： | 安徽中医学院,药学院,安徽,合肥,230031;安徽大学,物理与材料科学学院,安徽,合肥,230039 |
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| 基金项目： | 安徽省科技厅年度重点基金资助项目(01041188)，安徽省省级重点课程“普通物理”建设基金资助项目 |
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| 摘 要： | 从Legendre椭圆积分和Jacob i椭圆函数的定义出发,得到了新的变换,并把它用于非线性Schr d inger方程、KdV方程和BBM方程的求解中.这种Jacob i椭圆函数和三角函数的转换,既简化了求解过程,又能够得到周期解和孤波解,这样便于复杂方程的求解.
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| 关 键 词： | Jacobi椭圆函数 非线性波方程 周期解 孤波解 |
| 文章编号： | 1000-2162f2006）01-0058-05 |
| 收稿时间： | 2004-07-13 |
| 修稿时间： | 2004-07-13 |
A new method to construct periodic solutions to nonlinear wave equations |
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| QIAN Tian-hong,LIU Zhong-fei,HAN Jia-hua. A new method to construct periodic solutions to nonlinear wave equations[J]. Journal of Anhui University(Natural Sciences), 2006, 30(1): 58-62 |
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| Authors: | QIAN Tian-hong LIU Zhong-fei HAN Jia-hua |
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| Affiliation: | 1. Department of Pharmacy, Anhui College of Traditional Chinese Medicine, Hefei 230031, China ; 2. School of Physics and Material Science, Anhui University, Hefei 230039,China |
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| Abstract: | In the paper,from the definition of Legendre elliptic integration and Jacobi elliptic function,new transformations are obtained and applied to construct the exact solutions of nonlinear Schrdinger equation,KdV equation and BBM equation.There new analytical solutions such as periodic solutions and soliton solutions are derived for these nonlinear wave equations. |
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| Keywords: | Jacobi elliptic function nonlinear wave equation periodic solution solitary wave solution |
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