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KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS
Sun, Xiaowei; Wang, Youde
2011-10-01
Source PublicationINTERNATIONAL JOURNAL OF MATHEMATICS
ISSN0129-167X
Volume22Issue:10Pages:1439-1500
AbstractIn 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.
KeywordKdV geometric flow conversation law semi-conversation law Hasimoto transformation geometric energy method
DOI10.1142/S0129167X11007276
Language英语
Funding Project973 project of China[2006CB805902] ; NSFC[10990013]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000296619100004
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13135
Collection数学所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Sun, Xiaowei,Wang, Youde. KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2011,22(10):1439-1500.
APA Sun, Xiaowei,&Wang, Youde.(2011).KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS.INTERNATIONAL JOURNAL OF MATHEMATICS,22(10),1439-1500.
MLA Sun, Xiaowei,et al."KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS".INTERNATIONAL JOURNAL OF MATHEMATICS 22.10(2011):1439-1500.
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