Chong SONG1; You De WANG2
Source Publicationactamathematicasinicaenglishseries
AbstractIn 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 SchrSdinger soliton solution to the hyperbolic Ishimori system.
Document Type期刊论文
Affiliation1.LMAM,School of Mathematical Sciences,Peking University
Recommended Citation
GB/T 7714
Chong SONG,You De WANG. schrodingersolitonfromlorentzianmanifolds[J]. actamathematicasinicaenglishseries,2011,27(8):1455.
APA Chong SONG,&You De WANG.(2011).schrodingersolitonfromlorentzianmanifolds.actamathematicasinicaenglishseries,27(8),1455.
MLA Chong SONG,et al."schrodingersolitonfromlorentzianmanifolds".actamathematicasinicaenglishseries 27.8(2011):1455.
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