应用数学和力学2013，Vol.34Issue(9)：995-1002,8.DOI:10.3879/j.issn.1000-0887.2013.09.013
构造Birkhoff函数(组)的参数调节法
Parameter-Adjusting Method of Constructing Birkhoffian Functions
摘要
Abstract
The parameter-adjusting method to construct dynamical functions of Birkhoff' s equations is put forward based on realizing the completeness of Birkhoff' s equations,which are under-determinate,by means of Cauchy-Kovalevski integrability theorem for partial differential equations.The two kinds of parameters in the compensatory equation were capable of adjusting to get different sets of Birkhoffian functions.The existing methods,such as Hojman' s method using 2n first integrals for dynamical systems with symmetry,were compared with the parameter-adjusting method.Finally,The compensatory equation for the Birkhoff' s equations can be simplified by means of some limitations on the two kinds of parameters,where the relation between the Birkhoffian functions and parameters become more evident.关键词
Birkhoff方程/Cauchy-Kovalevski定理/自伴随微分方程/参数调节法Key words
Birkhoff's equations/ Cauchy-Kovalevski theorem/ self-adjoint differential equations/ parameter-adjusting method分类
数理科学引用本文复制引用
宋端,刘畅,郭永新..构造Birkhoff函数(组)的参数调节法[J].应用数学和力学,2013,34(9):995-1002,8.基金项目
The National Natural Science Foundation of China(11172120 （）
11202090 （）
10932002) （）
国家自然科学基金资助项目(11172120 （）
11202090 （）
10932002) （）
