Kac-Moody-Virasoro可积系统  

Kac-Moody-Virasoro integrable system

作　　者：赵启亮 贾曼[1,2] 楼森岳[1,2] ZHAO Qiliang;JIA Man;LOU Senyue(School of Physical Science and Technology,Ningbo University,Ningbo 315211,China;Laboratory of Clean Energy Storage and Conversion,Ningbo Univeristy,Ningbo 315211,China)

机构地区：[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

出　　处：《宁波大学学报（理工版）》2020年第5期83-92,共10页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11975131,11675084);宁波市自然科学基金(2015A610159);宁波大学王宽诚幸福基金。

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.By studying the symmetry of Kadomtse-Petviashvilli(KP)equation,we obtain the infinitedimensional 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.

关 键 词：李群 李代数 Kac-Moody-Virasoro代数 KP方程组 CK直接法 可积性 

分 类 号：O415[理学—理论物理]