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Kaup-Newell族的分数阶非线性双可积耦合及其Hamilton结构
引用本文:魏含玉,李春丽,夏铁成.Kaup-Newell族的分数阶非线性双可积耦合及其Hamilton结构[J].数学杂志,2017,37(3):580-590.
作者姓名:魏含玉  李春丽  夏铁成
作者单位:周口师范学院数学与统计学院, 河南 周口 466001,周口师范学院数学与统计学院, 河南 周口 466001,上海大学数学系, 上海 200444
基金项目: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.

关 键 词:矩阵Lie代数  Kaup-Newell族  双可积耦合  分数阶Hamilton结构
收稿时间:2015/12/2 0:00:00
修稿时间:2016/4/20 0:00:00

THE FRACTIONAL NOLINEAR BI-INTEGRABLE COUPLINGS OF KAUP-NEWELL HIERARCHY AND ITS HAMILTONIAN STRUCTURES
WEI Han-yu,LI Chun-li and XIA Tie-cheng.THE FRACTIONAL NOLINEAR BI-INTEGRABLE COUPLINGS OF KAUP-NEWELL HIERARCHY AND ITS HAMILTONIAN STRUCTURES[J].Journal of Mathematics,2017,37(3):580-590.
Authors:WEI Han-yu  LI Chun-li and XIA Tie-cheng
Institution:College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China,College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China and Department of Mathematics, Shanghai University, Shanghai 200444, China
Abstract: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.
Keywords:matrix Lie algebras  Kaup-Newell hierarchy  bi-integrable couplings  fractional Hamiltonian structures
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