| Broer-Kaup-Kupershmidt族的非线性双可积耦合及其自相容源 |
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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(A辑),2017,32(2). |
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| 作者姓名： | 魏含玉 夏铁成 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，河南省教育厅资助项目 |
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| 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.
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| 关 键 词： | 矩阵李代数 Broer-Kaup-Kupershmidt族 非线性双可积耦合 自相容源 |
Nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources |
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| WEI Han-yu,XIA Tie-cheng.Nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources[J].Applied Mathematics A Journal of Chinese Universities,2017,32(2). |
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| Authors: | WEI Han-yu XIA Tie-cheng |
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| 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 struc-tures 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. |
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| Keywords: | matrix Lie algebras Broer-Kaup-Kupershmidt hierarchy nonlinear bi-integrable couplings self-consistent sources |
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