广义耦合方程的延拓结构  

Prolongation Structures of Generalized Coupled Equation

作　　者：白喜瑞 Bai Xirui(Center for Nonlinear Studies,Ningbo University,Zhejiang Ningbo 315211)

机构地区：[1]宁波大学非线性研究中心,浙江宁波315211

出　　处：《数学物理学报（A辑）》2018年第4期658-670,共13页Acta Mathematica Scientia

摘　　要：该文利用延拓结构理论及单(半单)Lie代数的性质,研究了两组对偶系统的延拓结构.并且利用Lie代数表示理论,给出了两组对偶系统的Lax对表示.对于Camassa-Holm(CH)型的方程,通过对其超定方程的分析,仅仅选择了阶数小于等于2的函数F进行讨论,然而经过计算与分析却只存在阶数为1的情况.In this paper,we adopt the theory of continuation structure and properties ofsimple or semi-simple Lie algebra and studied the prolongation structure for two dual systems.Furthermore,the Lax pair of these equations are obtained by the method of Lie representationtheory.Considering the CH type equation,based on analysing its det ermined equations,we.select the functions F'that ord(F)≤2.However,there merely exists one order situationthrough calculation and analysis.

关 键 词：广义耦合方程 延拓结构 对偶系统 LAX对 

分 类 号：O175.2[理学—数学]