广义耦合方程的延拓结构

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 658-670.

广义耦合方程的延拓结构

白喜瑞

宁波大学非线性研究中心浙江宁波 315211

收稿日期:2017-05-31 修回日期:2017-10-16 出版日期:2018-08-26 发布日期:2018-08-26
作者简介:白喜瑞,E-mail:15729216969@163.com

Prolongation Structures of Generalized Coupled Equation

Bai Xirui

Center for Nonlinear Studies, Ningbo University, Zhejiang Ningbo 315211

Received:2017-05-31 Revised:2017-10-16 Online:2018-08-26 Published:2018-08-26

摘要/Abstract

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.

关键词: 广义耦合方程, 延拓结构, 对偶系统, Lax对

Abstract: In this paper, we adopt the theory of continuation structure and properties of simple 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 representation theory. Considering the CH type equation, based on analysing its determined equations, we select the functions F that ord(F) ≤ 2. However, there merely exists one order situation through calculation and analysis.

Key words: Generalized coupled equation, Prolongation structure, Dual system, Lax pair

中图分类号:

O175.2

白喜瑞. 广义耦合方程的延拓结构[J]. 数学物理学报, 2018, 38(4): 658-670.

Bai Xirui. Prolongation Structures of Generalized Coupled Equation[J]. Acta mathematica scientia,Series A, 2018, 38(4): 658-670.

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