Schrödinger flow of maps into symplectic manifolds

The definition of Schrödinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrödinger flow of maps intoS2, and that there exists a unique local smooth solution for the initial value problem of one-dimensional Schrödinger flow of maps into Kahler manifolds. In c...

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Bibliographic Details
Published inScience China. Mathematics Vol. 41; no. 7; pp. 746 - 755
Main Authors Ding, Weiyue, Wang, Youde
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.07.1998
Subjects
Boundary value problems
Ferromagnetism
Flow mapping
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Summary:The definition of Schrödinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrödinger flow of maps intoS2, and that there exists a unique local smooth solution for the initial value problem of one-dimensional Schrödinger flow of maps into Kahler manifolds. In case the targets are Kähler manifolds with constant curvature, it is proved that one-dimensional Schrödinger flow admits a unique global smooth solution.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1006-9283
1674-7283
1862-2763
1869-1862
DOI:10.1007/BF02901957