高维可积模型构造和解析解
PDF下载 (7104)林 机.高维可积模型构造和解析解[J].宁波大学学报(理工版),2020,33(5):3-7.DOI:
LIN Ji.High-dimensional integrable model construction and analytical solution[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(5):3-7.DOI:
| Title: | High-dimensional integrable model construction and analytical solution |
| 作者: | 林 机 |
| Author(s): | LIN Ji |
| 关键词: | Virasoro对称代数; 高维模型; 解析解; 可积性 |
| Keywords: | Virasoro symmetric algebra; higher-dimensional integrable model; exact solutations; integrability |
| 分类号: | O411 |
| 文献标识码: | A |
| 摘要: | 根据Virasoro可积性(具有无限维无中心Virasoro型对称代数意义下的可积性)的定义建立了一种系统构造(3+1)维Virasoro可积模型的方法. 利用广义Virasoro型对称代数的每一种具体实现, 可以得到大量的高维Virasoro意义下可积模型. 同时, 还获得了具有共形不变性、Painlevé和Lax对意义下的高维可积方程. 最后, 研究了部分方程的解析解. |
| Abstract: | On the basis of the definition of Virasoro’s integrability (with infinite dimensional and no-center Virasoro-type symmetric algebra), the method of constructing higher-dimension Virasoro of integrable model is presented. A large number of higher-dimensions integrable models can be obtained through each of specific realizations of the generalized Virasoro-type symmetric algebra. In addition, the high-dimensional integrable equations with conformally invariance, Painlevé and Lax pair are also obtained. Finally, the analytical solutions of some equations are studied. |
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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（10571086）. 作者简介: 林机（1965－）, 女, 浙江永康人, 教授, 主要研究方向: 孤立子与可积系统. E-mail: linji@zjnu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
