| 构造非线性演化方程精确解新方法 |
| |
| 引用本文： | 夏铁成,张鸿庆,闫振亚.构造非线性演化方程精确解新方法[J].大连理工大学学报,2001,41(3):260-263. |
| |
| 作者姓名： | 夏铁成 张鸿庆 闫振亚 |
| |
| 作者单位： | 大连理工大学应用数学系 |
| |
| 基金项目： | 国家重点基础研究发展规划资助项目! (G19980 30 6 0 0 )，国家自然科学基金资助项目! (10 0 72 0 13)，高等学校博士学科点专项科研基 |
| |
| 摘 要： | 借助于Mathematica和吴方法，运用双曲函数方法，获得了一类KdV-Burgers和KdV方程的多组精确行波解，其中包括新的奇性孤波解和新周期解，这个算法也可用于解其他的非线性偏微分方程，如变量Boussinesq方程组，非线性浅水长波近似方程组等，这个算法可以部分地在计算机上完成。
|
| 关 键 词： | 双曲函数 周期解 KdV－Burgers方程 吴方法 行波解 孤波解 非线偏微分方程 |
| 文章编号： | 1000-8608(2001)03-0260-04 |
A new approach to construct exact solutions of nonlinear evolution equations |
| |
| XIA Tie cheng ,ZHANG Hong qing ,YAN Zhen ya.A new approach to construct exact solutions of nonlinear evolution equations[J].Journal of Dalian University of Technology,2001,41(3):260-263. |
| |
| Authors: | XIA Tie cheng ZHANG Hong qing YAN Zhen ya |
| |
| Affiliation: | XIA Tie cheng 1,2,ZHANG Hong qing 1,YAN Zhen ya 1 |
| |
| Abstract: | With the aid of Mathematica and Wu elimination method, several types of explicit and exact travelling wave solutions for a system of KdV Burgers and KdV equations are obtained by hyperbolit function method. These solutions contain new singular solitary and new periodic solutions. The method can also be applied to solve some other systems of nonlinear partial differential equations, such as variant Boussinesq and the nonlinear approximate equations for long wave in shallow water. Some steps of this algorithm can be carried out by computer. |
| |
| Keywords: | hyperbolic functions periodic solution/ KdV Burgers equation Wu elimination method travelling wave solution solitary wave solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
