A Kind of Generalized Integrable Couplings and Their Bi-Hamiltonian Structure
A Kind of Generalized Integrable Couplings and Their Bi-Hamiltonian Structure
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DOI：
10.1007/s10773-021-04799-9
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发表时间：
2021-04
影响因子：
1.4
通讯作者：
Haifeng Wang;Yufeng Zhang
中科院分区：
文献类型：
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作者：
Haifeng Wang;Yufeng Zhang
我们引入了李代数，它可以用来构造一些谱问题的可积耦合。作为两个例子，非半简单李代数应用于扩大扩展 Ablowitz-Kaup-Newell-Segur (AKNS) 谱问题和广义 D-Kaup-Newell (D-KN) 谱问题的谱问题。由此可见，我们通过求解这些扩展的零曲率方程获得了两个广义可积耦合。最后，我们发现我们获得的可积层次结构具有组合形式的双哈密尔顿结构，从而显示了它们的刘维尔可积性。
We introduce a Lie algebrawhich can be used to construct integrable couplings of some spectral problems. As two examples, the non-semisimple Lie algebrais applied to enlarge the spectral problems of an extended Ablowitz-Kaup-Newell-Segur (AKNS) spectral problem and a generalized D-Kaup-Newell (D-KN) spectral problem. It follows that we obtain two generalized integrable couplings by solving these expanded zero-curvature equations. Finally, we find that the integrable hierarchies that we obtain have bi-Hamiltonian structures of combinatorial form, thereby showing their Liouville integrability.