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Schrödinger flow of maps into symplectic manifolds

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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.

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References

  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.

    MathSciNet  Google Scholar 

  2. Kenig, C. E., Ponce G., Vega, L., Small solutions to nonlinear Schrödinger equations,Anal. Nonlinéare, 1993, 10(3):255.

    MATH  MathSciNet  Google Scholar 

  3. Bourgain, J., Exponential sums and nonlinear Schrödinger equations,Geom. Funct. Anal., 1993, 3: 157.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  5. Amann, H., Quasilinear parabolic systems under nonlinear boundary conditions,Arch. Rat. Mech. Anal., 1986, 92:153.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Weiyue Ding & Youde Wang

Authors
  1. Weiyue Ding
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  2. Youde Wang
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Additional information

Project partially supported by the National Natural Science Foundation of China (Grant No. 19631020, 19701034).

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Ding, W., Wang, Y. Schrödinger flow of maps into symplectic manifolds. Sci. China Ser. A-Math. 41, 746–755 (1998). https://doi.org/10.1007/BF02901957

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  • DOI: https://doi.org/10.1007/BF02901957

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