非交换无色散Gelfand-Dickey方程族的附加对称  

Additional symmetry of noncommutative dispersionless Gelfand-Dickey hierarchy

作　　者：胡美艳 李传忠 HU Meiyan;LI Chuanzhong(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2021年第3期35-38,共4页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(12071237).

摘　　要：本文主要研究非交换无色散Gelfand-Dickey(GD)方程族的附加对称,给出它的Lax函数及方程,定义Orlov-Schulman函数M和附加流.在GD方程族约束情况下,找出非交换无色散GD方程族附加流中的存活流,同时研究特殊流得到弦方程并证明其形成一个无穷维李代数W_(1+∞).This article mainly deals with the additional symmetry of the noncommutative dispersionless Gelfand-Dickey(GD)hierarchy.We give its Lax function and equation,and define the Orlov-Schulman function M and the additional flows.Under the constraints of the GD hierarchy,we find that only a part of additional flows can survive.Considering the special additional flow,the string equation is obtained.In addition,this part of additional flow forms an infinite-dimensional Lie algebra 1 W_(1+∞).

关 键 词：附加对称 非交换无色散Gelfand-Dickey(GD)方程族 存活流 弦方程 

分 类 号：O175.2[理学—数学]