| THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS （III） |
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| 作者姓名： | Tu Guizhang Xu Baozhi |
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| 作者单位： | TU GUIZHANG * XU BAOZHIComputing Center of Academia Sinica，Beijing100080，China. **Department of Applied Mathematics，ZhejiangUniversity，Hangzhou 310027，China |
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| 基金项目： | ProjectsupportedbytheNationalNaturalScienceFoundationthroughNankaiInstituteofMathematics |
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| 摘 要： | §1.ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｈｅｏｒｙｏｆｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｏｆｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎｓｈａｓｕｎｄｅｒｇｏｎｅａｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｓｉｎｃｅｔｈｅｌａｔｅ1960’ｓ(ｓｅｅａｓｈｏｒｔｓｕｒｖｅｙｉｎ1]ａｎｄｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ).ＢｏｔｈｔｈｅｆｉｎｉｔｅａｎｄｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｈａｖｅｂｒｏａｄａｐｐｌｉｃａｔｉｏｎｓｉｎｖａｒｉｏｕ…
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| 关 键 词： | 可积分系统 哈密尔顿构造 迹恒定 线性发展方程 |
| 收稿时间： | 1993/9/16 0:00:00 |
THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS (III) |
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| Tu Guizhang,Xu Baozhi.THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS (III)[J].Chinese Annals of Mathematics,Series B,1996,17(4):497-506. |
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| Authors: | Tu Guizhang and Xu Baozhi |
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| Institution: | [1]ComputingCenterofAcademiaSinica,Beijing100080,China. [2]DepartmentofAppliedMathematics,ZhenjiangUniversity,Hangzhou310027,China. |
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| Abstract: | Two isospectral-problems, that contain three potential $u, v$
and $w$, are discussed. The corresponding hierarchies of
nonlinear evolution equations are derived. It is shown that both the two hierarchies of equations share a common interesting character that they admit a nonlinear reduction $w=\ga u v$ between the potentials with $\ga$ being a constant. In both the reduction cases the relevant Hamiltonian structures are established by using trace identity. |
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| Keywords: | Integrable system Hamiltonian structure Trace identity |
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