SchrSdinger Soliton from Lorentzian Manifolds

In this paper, we introduce a new notion named as SchrSdinger soliton. The so-called SchrSdinger solitons are a class of solitary wave solutions to the SchrSdinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a K//hler manifold N. If the target manifold N admits a Killing...

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Bibliographic Details
Published in数学学报：英文版 Vol. 27; no. 8; pp. 1455 - 1476
Main Author Chong SONG You De WANG
Format Journal Article
LanguageEnglish
Published 2011
Subjects
Cauchy问题
地图系统
孤子解
局部适定性
应用程序
洛仑兹
类孤波解
黎曼流形
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Summary:In this paper, we introduce a new notion named as SchrSdinger soliton. The so-called SchrSdinger solitons are a class of solitary wave solutions to the SchrSdinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a K//hler manifold N. If the target manifold N admits a Killing potential, then the SchrSdinger soliton reduces to a harmonic map with potential from M into N. Especially, when the domain manifold/~r is a Lorentzian manifold, the Schr6dinger soliton is a wave map with potential into N. Then we app][y 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 SchrSdinger soliton solution to the hyperbolic Ishinmri system.
Bibliography:Schr6dinger soliton, Schr6dinger flow, wave map, Killing potential
11-2039/O1
In this paper, we introduce a new notion named as SchrSdinger soliton. The so-called SchrSdinger solitons are a class of solitary wave solutions to the SchrSdinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a K//hler manifold N. If the target manifold N admits a Killing potential, then the SchrSdinger soliton reduces to a harmonic map with potential from M into N. Especially, when the domain manifold/~r is a Lorentzian manifold, the Schr6dinger soliton is a wave map with potential into N. Then we app][y 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 SchrSdinger soliton solution to the hyperbolic Ishinmri system.
ISSN:1439-8516
1439-7617