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| 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 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:Supported by National Natural Science Foundation of China (11547175; 11271008; 11501526); The Key Scientific Research Projects of Henan Province (16A110026). |
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| THE FRACTIONAL NOLINEAR BI-INTEGRABLE COUPLINGS OF KAUP-NEWELL HIERARCHY AND ITS HAMILTONIAN STRUCTURES |
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WEI Han-yu,LI Chun-li,XIA Tie-cheng
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| 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. |
| Key words: matrix Lie algebras Kaup-Newell hierarchy bi-integrable couplings fractional Hamiltonian structures |
