|本期目录/Table of Contents|

基于向量型李代数的方程族可积耦合及其哈密顿结构研究(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2020年03期
页码:
225-234
栏目:
研究论文
出版日期:
2020-05-15

文章信息/Info

Title:
 Vector-form Lie Algebras for Constructing Integrable Couplings of Hierarchies and Their Hamiltonian Structures
作者:
 杨启航1刘全生2
 1.山东科技大学数学与系统科学学院,山东 青岛 266590; 2.内蒙古大学数学科学学院,呼和浩特 010021
Author(s):
YANG Qi-hang1LIU Quan-sheng2
 1.College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China;
2.School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China
关键词:
 向量型李代数 线性和非线性可积耦合 双哈密顿结构
Keywords:
 Vector-form Lie Algebra linear and nonlinear integrable coupling bi-Hamiltonian structure
分类号:
-
DOI:
-
文献标识码:
A
摘要:
构造了几个6维向量型李代数及其相应的LOOP代数,获得了Burgers方程族的线性和非线性可积耦合以及其哈密顿结构。进一步,将上述6维李代数推广到9维向量型李代数,研究了Dirac族耦合的可积耦合。利用迹恒等式,得到了上述系统的哈密顿结构和双哈密顿结构。
Abstract:
 Several 6-dimensional vector-form Lie algebras and their corresponding loop Algebras are constructed to work out the linear and nonlinear integrable couplings,then the Lie algebras are enlarged to a 9-dimensional vector-form Lie algebra for studying the integrable couplings of the Dirac hierarchy coupling.By employing the variation identity,the Hamiltonian and bi-Hamiltonian structures of the above systems are obtained.

参考文献/References

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备注/Memo

备注/Memo:
收稿日期:2019-11-12
基金项目:国家自然科学基金 ( 11562014 ); 内蒙古自治区自然科学基金 ( 2017MS0108 )
作者简介:杨启航(1998-),男,山东青岛人。
通信作者:刘全生(1979-),内蒙古赤峰人,教授,博士。主要从事应用数学和流体力学的研究。E-mail:smslqs@imu.edu.cn
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