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Schrodinger soliton from Lorentzian manifolds
Song, Chong1; Wang, You De2
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 Schrodinger soliton solution to the hyperbolic Ishimori system.
KeywordSchrodinger soliton Schrodinger flow wave map Killing potential
Funding Project973 Project of China[2006CB805902]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000293233600001
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Document Type期刊论文
Corresponding AuthorSong, Chong
Affiliation1.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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