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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (2): 165-175    
    
Broer-Kaup-Kupershmidt族的非线性双可积耦合及其自相容源
魏含玉1 , 夏铁成2
1. 周口师范学院 数学与统计学院, 河南周口 466001
2. 上海大学 数学系, 上海 200444
Nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources
WEI Han-yu1 , XIA Tie-cheng2
1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China
2. Department of Mathematics, Shanghai University, Shanghai, 200444, China
 全文: PDF 
摘要： 基于新的非半单矩阵李代数, 介绍了构造孤子族非线性双可积耦合的方法, 由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构. 作为应用, 给出了Broer-Kaup-Kupershmidt族的非线性双可积耦合及其Hamilton结构. 最后指出了文献中的一些错误, 利用源生成理论建立了新的公式, 并导出了带自相容源Broer-Kaup-Kupershmidt族的非线性双可积耦合方程.
关键词： 矩阵李代数;  Broer-Kaup-Kupershmidt族;  非线性双可积耦合;  自相容源    
Abstract: Based on new non-semisimple matrix Lie algebras, the general method of constructing the nonlinear bi-integrable couplings of soliton hierarchy is introduced. The corresponding variational identity yields Hamiltonian structures of the resulting bi-integrable couplings. As an application, the nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy and their Hamiltonian structures are given. Finally, some errors exist in reference are pointed out, and a set of new formulae using the theory of source are set up, also the nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources is derived based on the new formulae.
Key words: matrix Lie algebras    Broer-Kaup-Kupershmidt hierarchy    nonlinear bi-integrable couplings    self-consistent sources
收稿日期: 2016-03-06 出版日期: 2017-06-01
基金资助: 国家自然科学基金(11547175; 11271008; 11501526); 河南省教育厅资助项目(13A110101)
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引用本文:

魏含玉, 夏铁成. Broer-Kaup-Kupershmidt族的非线性双可积耦合及其自相容源[J]. 高校应用数学学报, 2017, 32(2): 165-175.

WEI Han-yu, XIA Tie-cheng. Nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 165-175.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I2/165

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