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(王友德)Geometric solitons of Hamiltonian flows on manifolds
2013-11-22 | 编辑:

  论文题目:Geometric solitons of Hamiltonian flows on manifolds

  论文作者:Chong Song, Xiaowei Sun, Youde Wang(王友德)

  论文摘要:It is well-known that the LIE(Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schr\"odinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schr\"odinger flow and geometric KdV flow, including magnetic curves as geometric Schr\"odinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  所属学科:微分几何

  所属实验室或研究中心:数学研究所

  全文链接: http://arxiv.org/abs/1212.3934

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