Kaup-Newell族的分数阶非线性双可积耦合及其Hamilton结构
THE FRACTIONAL NOLINEAR BI-INTEGRABLE COUPLINGS OF KAUP-NEWELL HIERARCHY AND ITS HAMILTONIAN STRUCTURES

本文研究了Kaup-Newell族的分数阶非线性双可积耦合.利用分数阶等谱问题和非半单矩阵Lie代数上的非退化、对称双线性形式，得到了Kaup-Newell族的分数阶非线性双可积耦合，并求出了Kaup-Newell族双可积耦合的分数阶Hamilton结构.本文的方法还可以应用于其它孤子族分数阶可积耦合.
In this paper, we study the fractional nolinear bi-integrable couplings of KaupNewell hierarchy. By using fractional isospectral problems and non-semisimple matrix Lie algebras on which there exist non-degenerate, symmetric and ad-invariant bilinear forms, the fractional nonlinear bi-integrable couplings of Kaup-Newell hierarchy are presented. Furthermore, we also obtained the fractional Hamiltonian structures of the fractional integrable couplings of Kaup-Newell hierarchy. The methods derived by us can be generalized to other fractional integrable couplings of soliton hierarchy