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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (2): 165-175    DOI:
    
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
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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 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     
Received: 06 March 2016      Published: 01 June 2017
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WEI Han-yu
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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/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I2/165


Broer-Kaup-Kupershmidt族的非线性双可积耦合及其自相容源

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 
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