Davey-Stewartson系列的无色散化探讨  

Discussion on the Dispersionless Limit of Davey-Stewartson Hierarchy

作　　者：廖显金 易戈 LIAO Xian-jin;YI Ge(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2021年第5期37-41,共5页College Mathematics

摘　　要：从Davey-Stewartson(DS)系列的定义和性质出发,按照标准的无色散方法,研究了DS系列的无色散(半经典)极限.利用整个系列的特征函数的WKB表示,在无色散极限下,得到了无色散DS系列的哈密顿-雅可比型的非线性Lax表示,给出了无色散DS系列的流方程.最后,通过两个例子验证了结论的正确性.Based on the definition and properties of the Davey-Stewartson(DS)hierarchy,the dispersionless(semi-classical)limit of the DS hierachy is studied by following the standard dispersionless method.By taking advantage of the WKB form of the whole hierarchy’s eigenfunctions,the nonlinear Lax formulation of Hamilton-Jacobi type of dispersionless Davey-stewartson(dDS)hierarchy is obtained in the dispersionless limit.The flow equations of dDS hierarchy are given.Finally,two examples are provided to demonstrate the validity of the obtained results.

关 键 词：DS系列 半经典极限 WKB表示 流方程 

分 类 号：O175.3[理学—数学]