| 含外力项的广义KdV方程的新自Darboux变换和显式解析解 |
| |
| 引用本文： | 闫振亚,张鸿庆.含外力项的广义KdV方程的新自Darboux变换和显式解析解[J].数学研究及应用,2001,21(3):323-328. |
| |
| 作者姓名： | 闫振亚 张鸿庆 |
| |
| 作者单位： | 大连理工大学应用数学系, |
| |
| 基金项目： | Supported by the National Natural Science Foundation of China under the Grant (19572022), Doctoral Foundation of Education Ministry of China under the Grant
(98014119) and the National Key Basic Research Project under the Grant(G1998030600) |
| |
| 摘 要： | 基于 Ｒｉｃｃａｔｉ形式的 Ｌａｘ对，本文推得了含外力项的广义 ＫｄＶ方程的新自Ｄａｒｂｏｕｘ变换．当应用这个变换时，仅需要做积分，就能获得一系列显示解析解，其中包含类孤波解．这种途径对于寻找非线性发展方程新的具有物理意义的解或许是有用的．
|
| 关 键 词： | Riccati形式 Lax对 广义KdV方程 新自Darbowx变换 显示解析解 孤波解 |
| 文章编号： | 1000-341X(2001)03-0323-06 |
| 收稿时间： | 1999/10/26 0:00:00 |
| 修稿时间： | 1999年10月26 |
New Auto-Darboux Transformation and Explicit Analytic Solutions for the Generalized KdV Equation with External Force Term |
| |
| YAN Zhen-ya and ZHANG Hong-qing.New Auto-Darboux Transformation and Explicit Analytic Solutions for the Generalized KdV Equation with External Force Term[J].Journal of Mathematical Research with Applications,2001,21(3):323-328. |
| |
| Authors: | YAN Zhen-ya and ZHANG Hong-qing |
| |
| Institution: | Dept. of Appl. Math.; Dalian University of Technology; Dalian; China;Dept. of Appl. Math.; Dalian University of Technology; Dalian; China |
| |
| Abstract: | In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration is needed, a series of explicit analytic solutions can be obtained, which contain solitary-like wave solutions. This method may be important for seeking more new and physical signficant analytic solutions of nonlinear evolution equations. |
| |
| Keywords: | GKdV equation Lax pair Darboux transformation analytic solution solitary wave solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
