| On a Reduction of the Kadomtsev-Petviashvili Hierarchy |
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| 作者姓名： | 薛婷 |
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| 作者单位： | Department of |
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| 摘 要： | Introduction Many (1 1)-dimensional integrable systems can be re- duced from the Kadomtsev-Petviashvili (KP) hierarchy, with the most typical examples including the Gelfand- Dickey hierarchy (N-Korteweg de Vries (KdV) hierar- chy)1] and the so called con…
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| 关 键 词： | Kadomtsev-Petviashvili体系 双哈密尔顿结构 二维可积系统 KDV方程 |
| 收稿时间： | 2004-10-26 |
| 修稿时间： | 2004-10-26 |
On a Reduction of the Kadomtsev-Petviashvili Hierarchy |
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| Ting Xue,
.On a Reduction of the Kadomtsev-Petviashvili Hierarchy[J].Tsinghua Science and Technology,2006,11(1):111-116. |
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| Authors: | Ting Xue
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| Institution: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | This paper analyzes the reduction of the well known Kadomtsev-Petviashvili hierarchy. The reduction yields a previously unknown dispersion counterpart of the dispersionless hierarchy which has a Lax function of the form p+u(x)(p??)?1+v(x)(p??)?2. This paper also describes the bihamiltonian structure of the reduced hierarchy using Dirac reduction and proves that the approximation for the reduced hierarchy up to the second order of the dispersion parameter coincides with the hierarchy of integrable systems constructed from a particular two-dimensional Frobenius manifold using the approach of Dubrovin and Zhang. |
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| Keywords: | dispersionless Kadomtsev-Petviashvili hierarchy constrained Kadomtsev-Petviashvili hierarchy bigraded Toda hierarchy deformations of the hydrodynamic type bihamiltonian structure |
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