| Schrodinger soliton from Lorentzian manifolds | |
Song, Chong1; Wang, You De2
| |
| 2011-08-01 | |
| Source Publication | ACTA MATHEMATICA SINICA-ENGLISH SERIES
 |
| ISSN | 1439-8516 |
| Volume | 27Issue:8Pages:1455-1476 |
| Abstract | 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. |
| Keyword | Schrodinger soliton Schrodinger flow wave map Killing potential |
| DOI | 10.1007/s10114-011-0229-y |
| Language | 英语 |
| Funding Project | 973 Project of China[2006CB805902] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000293233600001 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/11862 |
| Collection | 数学所 |
| Corresponding Author | Song, Chong |
| Affiliation | 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 |
| Recommended Citation 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. |
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