Kaup-Newell族的分数阶非线性双可积耦合及其Hamilton结构（英文）  

THE FRACTIONAL NOLINEAR BI-INTEGRABLE COUPLINGS OF KAUP-NEWELL HIERARCHY AND ITS HAMILTONIAN STRUCTURES

作　　者：魏含玉[1] 李春丽[1] 夏铁成[2] 

机构地区：[1]周口师范学院数学与统计学院,河南周口466001 [2]上海大学数学系,上海200444

出　　处：《数学杂志》2017年第3期580-590,共11页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11547175;11271008;11501526);The Key Scientific Research Projects of Henan Province(16A110026)

摘　　要：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 Kaup- Newell 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.

关 键 词：矩阵Lie代数 Kaup-Newell族 双可积耦合 分数阶Hamilton结构 

分 类 号：O175.29[理学—数学]