基于扩展主对称方法的Kadomtsev-Petviashvilli方程的对称与无穷维李代数
PDF下载 (267)樊 荣,李 彪.基于扩展主对称方法的Kadomtsev-Petviashvilli方程的对称与无穷维李代数[J].宁波大学学报(理工版),2020,33(5):93-98.DOI:
FAN Rong,LI Biao.Extended master symmetry approach: Symmetries and infinite-dimensional Lie algebra of the Kadomtsev-Petviashvilli equation[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(5):93-98.DOI:
| Title: | Extended master symmetry approach: Symmetries and infinite-dimensional Lie algebra of the Kadomtsev-Petviashvilli equation |
| 作者: | 樊 荣, 李 彪 |
| Author(s): | FAN Rong, LI Biao |
| 关键词: | 对称; 李代数; 显式表达式 |
| Keywords: | symmetries; Lie algebra; explicit expression |
| 分类号: | O175.2 |
| 文献标识码: | A |
| 摘要: | 提出了扩展的主对称方法, 将它应用于2+1维可积模型—–Kadomtsev-Petviashvilli (KP)方程, 获得了该方程中含有时间 的任意函数的广义对称, 无需使用复杂的递归算子, 即可直接从对称定义方程中得出关于KP方程对称的显式简单构造公式. 本文中所有提到的对称都是此方程对称的特例, 同时, 还给出了由这些对称构成的一般无穷维李代数. |
| Abstract: | In this paper, an extended master symmetry method is proposed and applied to the (2+1)-dimensional integrable model Kadomtsev-Petviashvilli (KP) equation, and the generalized symmetry of any function containing time in the equation is obtained. Then an explicit and simple constructive formula for the symmetries of the KP equation is derived directly from the symmetry definition equation, in which the complicated recursion operators are skipped. All the known symmetries appear as special cases for those symmetries obtained in this work. The general infinite-dimensional Lie algebra constituted by these symmetries is also given. |
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| 备注/Memo: | 收稿日期: 2020－05－11. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11775121, 11435005）. 第一作者: 樊荣（1996－）, 女, 山西长治人, 在读硕士研究生, 主要研究方向: 非线性数学物理. E-mail: 1063680148@qq.com *通信作者: 李彪（1971－）, 男, 湖南会同人, 教授, 主要研究方向: 非线性数学物理. E-mail: libiao@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
