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	Schrodinger soliton from Lorentzian manifolds
	Song, Chong ; Wang, You De
	2011
关键词	Schrodinger soliton Schrodinger flow wave map Killing potential EINSTEIN-KAHLER-METRICS HARMONIC MAPS CAUCHY-PROBLEM FLOW EQUATIONS DIMENSIONS UNIQUENESS EXISTENCE SYSTEM SPACES
英文摘要	In this paper, we introduce a new notion named as Schrodinger soliton. The so-called Schrodinger solitons are a class of solitary wave solutions to the Schrodinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a Kahler manifold N. If the target manifold N admits a Killing potential, then the Schrodinger soliton reduces to a harmonic map with potential from M into N. Especially, when the domain manifold M is a Lorentzian manifold, the Schrodinger soliton is a wave map with potential into N. Then we apply the geometric energy method to this wave map system, and obtain the local well-posedness of the corresponding Cauchy problem as well as global existence in 1+1 dimension. As an application, we obtain the existence of Schrodinger soliton solution to the hyperbolic Ishimori system.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000293233600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 3; ARTICLE; 8; 1455-1476; 27
语种	英语
出处	SCI
出版者	acta mathematica sinica english series
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157582]
专题	数学科学学院
推荐引用方式 GB/T 7714	Song, Chong,Wang, You De. Schrodinger soliton from Lorentzian manifolds. 2011-01-01.

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