AKNS-KN孤子方程族的可积耦合与Hamilton结构 |
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引用本文: | 张玉峰 Fu Kui Guo.AKNS-KN孤子方程族的可积耦合与Hamilton结构[J].数学学报,2008,51(5):889-900. |
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作者姓名: | 张玉峰 Fu Kui Guo |
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作者单位: | 辽宁师范大学数学系 |
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摘 要: | 首先通过引入高维圈代数,在零曲率方程框架下得到了AKNS-KN孤子族(记为AKNS-KN-SH)的一个新的可积耦合系统;再由二次型恒等式得到了该系统的双-Hamilton结构形式.最后引进了一个新的Lie代数A_4,可通过建立其不同的圈代数与等价的列向量Lie代数,研究AKNS-KN-SH的多分量可积耦合系统及其Hamilton结构.
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关 键 词: | Hamilton结构 圈代数 可积耦合 |
收稿时间: | 2007-5-8 |
Integrable Couplings and Hamiltonian Structure of the AKNS-KN Soliton-Equation Hierarchy |
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Institution: | Mathematical School, Liaoning Normal University, Dalian 116029 Mathematical School, Liaoning Normal University, Dalian 116029 |
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Abstract: | By introducing a
higher-dimensional loop algebra, a new integrable coupling of the
AKNS-KN soliton hierarchy (called AKNS-KN-SH, for short) is
obtained under the framework of zero curvature equations, whose
Hamiltonian structure is worked out by using the quadratic-form
identity. Finally we give a new Lie algebra $A_4$ so that its
various loop algebras and its equivalent colummn-vector Lie
algebra are introduced respectively for which multi-component
integrable couplings and their Hamiltonian structure of the the
AKNS-KN-SH could be generated. |
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Keywords: | Hamiltonian structure loop algebra integrable couplings |
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