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| 利用李代数构造非线性可积及双可积哈密顿耦合 | |
| 引用本文： | 陈晓红,张鸿庆,尤福财,张大庆. 利用李代数构造非线性可积及双可积哈密顿耦合[J]. 数学研究及应用, 2015, 35(3): 291-302 |
| 作者姓名： | 陈晓红 张鸿庆 尤福财 张大庆 |
| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024; 辽宁科技大学理学院, 辽宁 鞍山 114051;大连理工大学数学科学学院, 辽宁 大连 116024;沈阳工程学院基础教学部, 辽宁 沈阳 110136;辽宁科技大学理学院, 辽宁 鞍山 114051 |
| 基金项目： | 国家自然科学基金 (Grant Nos.61273011; 11401392). |
| 摘 要： | With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system. |
| 关 键 词： | Lie algebra integrable couplings bi-integrable couplings Hamiltonian structure |
| 收稿时间： | 2014-03-24 |
| 修稿时间： | 2015-01-16 |
Lie Algebras for Constructing Nonlinear Integrable and Bi-Integrable Hamiltonian Couplings |
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| Xiaohong CHEN,Hongqing ZHANG,Fucai YOU and Daqing ZHANG. Lie Algebras for Constructing Nonlinear Integrable and Bi-Integrable Hamiltonian Couplings[J]. Journal of Mathematical Research with Applications, 2015, 35(3): 291-302 | |
| Authors: | Xiaohong CHEN Hongqing ZHANG Fucai YOU Daqing ZHANG |
| Affiliation: | Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China; School of Science, University of Science and Technology Liaoning, Liaoning 114051, P. R. China;Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China;Department of Basic Sciences, Shenyang Institute of Engineering, Liaoning 110136, P. R. China;School of Science, University of Science and Technology Liaoning, Liaoning 114051, P. R. China |
| Abstract: | With the help of a Lie algebra, two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings. For illustrating the application of the Lie algebras, an integrable Hamiltonian system is obtained, from which some reduced evolution equations are presented. Finally, Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity. The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system. |
| Keywords: | Lie algebra integrable couplings bi-integrable couplings Hamiltonian structure |
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