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  

Vector-form Lie Algebras for Constructing Integrable Couplings of Hierarchies and Their Hamiltonian Structures

作　　者：杨启航 刘全生[2] YANG Qi-hang;LIU Quan-sheng(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China;School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[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

出　　处：《内蒙古大学学报（自然科学版）》2020年第3期225-234,共10页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11562014);内蒙古自治区自然科学基金(2017MS0108)。

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。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-Hamiltonian structures of the above systems are obtained.

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 

分 类 号：O175[理学—数学] O152.5[理学—基础数学]