SchrSdinger Soliton from Lorentzian Manifolds  

作　　者：Chong SONG You De WANG 

机构地区：[1]LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China [2]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第8期1455-1476,共22页数学学报（英文版）

摘　　要：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.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.

关 键 词：Schr6dinger soliton Schr6dinger flow wave map Killing potential 

分 类 号：O186.12[理学—数学] O175.29[理学—基础数学]