中文摘要：

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．

英文摘要：

Based on new non-semisimple the nonlinear bi-integrable couplings of soliton matrix Lie algebras, the general method of constructing 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, aIso the nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources is derived based on the new formulae.