中文摘要：

本文基于新的非半单矩阵Lie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Kaup-Newell族的非线性双可积耦合及其Hamilton结构.最后利用源生成理论建立新的公式,并导出带自相容源Kaup-Newell族的非线性双可积耦合方程.

英文摘要：

Based on new non-semisimple matrix Lie algebras, we introduce the general method of constructing the nonlinear bi- integrable couplings of soliton hierarchy. The corresponding variational identity yields Hamiltonian structures of the resulting bi-integrable couplings. As an application, we give the nonlinear bi-integrable couplings of Kaup-Newell hierarchy and its Hamiltonian structures. Finally, we set up a set of new formulas using the theory of source, and the nonlinear bi-integrable couplings of Kaup-Newell hierarchy with self-consistent sources is derived based on the new formulas.