| KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS |
| Sun, Xiaowei; Wang, Youde
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| 2011-10-01
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发表期刊 | INTERNATIONAL JOURNAL OF MATHEMATICS
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ISSN | 0129-167X
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卷号 | 22期号:10页码:1439-1500 |
摘要 | In this paper, we define a kind of KdV (Korteweg-de Vries) geometric flow for maps from a real line R or a circle S(1) into a Kahler manifold (N, J, h) with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By Hasimoto transformation, we find that the KdV geometric flow on a Riemann surface of constant Gauss curvature is just classical complex-valued mKdV equation. From the view point of geometric analysis we show that the Cauchy problems of KdV flow on a Kahler manifold admits a unique local solution in suitable Sobolev spaces. In the case the target manifold (N, J, h) with complex structure J and metric h is a certain type of locally Hermitian symmetric space, we show that the KdV flow exists globally by exploiting the conservation laws and semi-conservation law of KdV flow. |
关键词 | KdV geometric flow
conversation law
semi-conversation law
Hasimoto transformation
geometric energy method
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DOI | 10.1142/S0129167X11007276
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语种 | 英语
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资助项目 | 973 project of China[2006CB805902]
; NSFC[10990013]
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WOS研究方向 | Mathematics
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WOS类目 | Mathematics
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WOS记录号 | WOS:000296619100004
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出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD
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引用统计 |
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文献类型 | 期刊论文
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条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/13135
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专题 | 数学所
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通讯作者 | Sun, Xiaowei |
作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
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推荐引用方式 GB/T 7714 |
Sun, Xiaowei,Wang, Youde. KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2011,22(10):1439-1500.
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APA |
Sun, Xiaowei,&Wang, Youde.(2011).KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS.INTERNATIONAL JOURNAL OF MATHEMATICS,22(10),1439-1500.
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MLA |
Sun, Xiaowei,et al."KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS".INTERNATIONAL JOURNAL OF MATHEMATICS 22.10(2011):1439-1500.
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