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Science in China Series A: Mathematics

, Volume 41, Issue 7, pp 746–755 | Cite as

Schrödinger flow of maps into symplectic manifolds

  • Weiyue Ding
  • Youde Wang
Article

Abstract

The definition of Schrödinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrödinger flow of maps intoS 2, 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.

Keywords

Schrödinger flow Kähler manifold conservative law sectional curvature 

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References

  1. 1.
    Zhou., Y., Guo, Tan, S., Existence and uniqueness of smooth solution for system of ferromagnetic chain,Science in China Ser. A, 1991, 34: 257.MathSciNetGoogle Scholar
  2. 2.
    Kenig, C. E., Ponce G., Vega, L., Small solutions to nonlinear Schrödinger equations,Anal. Nonlinéare, 1993, 10(3):255.zbMATHMathSciNetGoogle Scholar
  3. 3.
    Bourgain, J., Exponential sums and nonlinear Schrödinger equations,Geom. Funct. Anal., 1993, 3: 157.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bourgain, J., Fourier transfrm restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, I. Schrödinger equations,Geom. Funct. Anal., 1993, 3: 107.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Amann, H., Quasilinear parabolic systems under nonlinear boundary conditions,Arch. Rat. Mech. Anal., 1986, 92:153.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science in China Press 1998

Authors and Affiliations

  • Weiyue Ding
    • 1
  • Youde Wang
    • 1
  1. 1.Institute of MathematicsChinese Academy of SciencesBeijingChina

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