B类Kadomtsev-Petviashvili非线性系统的弦方程和Virasoro约束  

The String Equation of the B-type Kadomtsev-Petviashvili Hierarchy and Virasoro Constraint

作　　者：倪雨星 刘少伟[1] NI Yuxing;LIU Shaowei(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2023年第5期14-21,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11101338).

摘　　要：主要研究B类Kadomtsev-Petviashvili(BKP)非线性系统的弦方程以及弦方程加在该系统τ函数上的约束所形成的Lie代数.首先,通过对现有文献分析,发现BKP系统弦方程的定义会产生数学上的矛盾,因此在现有文献的基础上重新优化了BKP系统弦方程的定义.然后从此定义出发重新计算了弦方程的附加对称算子表达式,进一步算出弦方程约束在BKP系统波函数和τ函数上的表达式.由于p约化的约束需要去掉冗余变量,因此给出了弦方程加在p约化BKP系统的τ函数上所生成的无冗余变量的约束算子.最后,通过复杂的计算,低阶弦方程无冗余约束算子恰好能形成一个被广泛研究的经典无穷维Lie代数,即非负的Virasoro代数和W代数.其展现了BKP系统良好的代数结构,与现有经典结果相容.In this paper,the string equation of the B-type Kadomtsev-Petviashvili(BKP)hierarchy and the Lie algebra formed by the constraints imposed by the string equation on theτfunction of the hierarchy are mainly studied.Firstly,through the analysis of the existing literature,it is found that the definition of the string equation of the BKP hierarchy will produce a mathematical contradiction.Therefore,this paper re-optimizes the definition of the string equation of the BKP hierarchy on the basis of the existing literature.Then,from this definition,the additional symmetry operator expressions of the string equation are recalculated,and the expressions of the string equation constrained on the BKP hierarchy wave function and theτfunction are further calculated.Because of the constraints of the p reduction,it is natural to remove redundant variables.Therefore,different from the existing results,this paper presents the string equation constraint operators without redundant variables,which are imposed by the string equation on theτfunction of the p-reduced BKP hierarchy.Finally,through complex calculations,it is found that low-order string equation constraint operators without redundant variables can precisely form a widely studied classical infinite-dimensional Lie algebra,namely,the non-negative Virasoro algebra and W algebra.It shows the good algebraic structure of the BKP hierarchy,which is compatible with the existing classical results.This also shows that our optimized definition of the string equation for the BKP hierarchy is reasonable from another perspective.

关 键 词：BKP系统 附加对称 弦方程 VIRASORO代数 

分 类 号：O175[理学—数学]