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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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