扩展的Dirac族及其可积耦合  

A Generalized Dirac Soliton Hierarchy and Its Integrable Couplings

作　　者：关雪[1] 朱宏伟[1] 张辉群[1] 

机构地区：[1]青岛大学数学与统计学院,青岛266071

出　　处：《青岛大学学报（自然科学版）》2017年第2期4-8,共5页Journal of Qingdao University(Natural Science Edition)

基　　金：山东省自然科学基金(批准号:ZR2015FM023)资助

摘　　要：构造可积族的可积耦合系统极大地丰富了可积系统理论,成为研究的热点问题。基于一个具有双哈密顿结构的扩展的Dirac可积族,利用李代数半直和分解的思想,引入一类特殊的非半单矩阵Loop代数,得到该可积族的可积耦合系统。并利用变分恒等式证明了该可积耦合系统具有哈密顿结构。The integrable coupl ing of the integrable system has great ly enriched the theory of integrable systems, which has become a hot issue in the research. Based on an extended Dirac integrable hierarchy with Bi-Hamiltonian structures, a special class of non-semisimple matrix Loop algebras is introduced by using the theory of Lie algebra and semi-direct sums decomposition. By using the variational equation, it is proved that the integrable coupling system has Hamiltonian structure.

关 键 词：LOOP代数 可积方程族 双HAMILTON结构 可积耦合 

分 类 号：O179.29[理学—数学]