Schrodinger soliton from Lorentzian manifolds

doi:10.1007/s10114-011-0229-y

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	Schrodinger soliton from Lorentzian manifolds
	Song, Chong 1; Wang, You De2
	2011-08-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	27 期号:8 页码:1455-1476
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.
关键词	Schrodinger soliton Schrodinger flow wave map Killing potential
DOI	10.1007/s10114-011-0229-y
语种	英语
资助项目	973 Project of China[2006CB805902]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000293233600001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11862
专题	数学所
通讯作者	Song, Chong
作者单位	1.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Song, Chong,Wang, You De. Schrodinger soliton from Lorentzian manifolds[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2011,27(8):1455-1476.
APA	Song, Chong,&Wang, You De.(2011).Schrodinger soliton from Lorentzian manifolds.ACTA MATHEMATICA SINICA-ENGLISH SERIES,27(8),1455-1476.
MLA	Song, Chong,et al."Schrodinger soliton from Lorentzian manifolds".ACTA MATHEMATICA SINICA-ENGLISH SERIES 27.8(2011):1455-1476.