| Kac-Moody-Virasoro可积系统 |
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| 引用本文： | 赵启亮,贾曼,楼森岳. Kac-Moody-Virasoro可积系统[J]. 宁波大学学报(理工版), 2020, 33(5): 83-92 |
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| 作者姓名： | 赵启亮 贾曼 楼森岳 |
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| 作者单位： | 1.宁波大学 物理科学与技术学院, 浙江 宁波 315211; 2.宁波大学 清洁能源存储与转换实验室, 浙江 宁波 315211 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金;宁波市自然科学基金;宁波大学王宽诚幸福基金 |
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| 摘 要： | 通过研究Kadomtsev-Petviashvilli(KP)方程对称, 得到相应的无穷维李代数—–Kac-Moody- Virasoro(KMV)代数, 并运用KMV代数的生成元和其中一个子代数—–Virasoro代数的延拓结构, 推导出熟知的Kadomtsev-Petviashvilli(KP)方程, 并以此为基础得到更多高阶(2+1)维和(3+1)维的可积模型, 并且这些模型都具有KMV代数性质.
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| 关 键 词： | 李群 李代数 Kac-Moody-Virasoro代数 KP方程组 CK直接法 可积性 |
Kac-Moody-Virasoro integrable system |
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| ZHAO Qiliang1,' target="_blank" rel="external">2,JIA Man1,' target="_blank" rel="external">2,LOU Senyue1,' target="_blank" rel="external">2. Kac-Moody-Virasoro integrable system[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2020, 33(5): 83-92 |
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| Authors: | ZHAO Qiliang1,' target=" _blank" rel=" external" >2,JIA Man1,' target=" _blank" rel=" external" >2,LOU Senyue1,' target=" _blank" rel=" external" >2 |
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| Affiliation: | 1.School of Physical Science and Technology, Ningbo University, Ningbo 315211, China; 2.Laboratory of Clean Energy Storage and Conversion, Ningbo Univeristy, Ningbo 315211, China |
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| Abstract: | By studying the symmetry of Kadomtse-Petviashvilli (KP) equation, we obtain the infinite- dimensional Lie algebra of symmetries, which is termed as Kac-Moody-Virasoro (KMV) algebra. Using generators of KMV algebra and the prolongation of Virasoro algebra, the Kadomtse-Petviashvilli (KP) equation is obtained. In addition, the other higher order (2+1)-dimensional and (3+1)-dimensional integrable model can thus be derived from KP equation. It is worth noting that all the models possess the same properties of KMV algebra. |
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| Keywords: | Lie group of symmetries Lie algebra Kac-Moody-Virasoro algebra KP equtions CK direct method integrability |
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