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.
