| LIE GROUPS ADMITTED BY AUTONOMOUSSYSTEM WITH GIVEN STRUCTURECONSTANTS |
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| 作者姓名： | 雷锦志 管克英 |
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| 作者单位： | LeiJinzhi(Dept. of Math.，Beijing University of Aeronautics and Astronautics，Beijing 100083)Guan Keying (Dept. of Math.，Northern Jiaotong University，Beijing 100044) |
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| 摘 要： | 1IlltroductionandNotationsInthesecondhalfofthepreviouscentury,SophousLieintroducedthetheoryofLiegroups,inordertocreateatheoryofintegratingordinarydifferentialequations.Sofar,Liegrouptheoryhadplayedimportantimpactinintegrabilitytheoryofdifferentialequations(ref.l,2,3]).Considerthefollowingfirstorderautonomoussystemofnordinarydifferentialequations'wherex=(x',x','3x")ED,andDisasub-domainofR"(orC"),XifD-- R(orC),XfECoo(D),andtER(orC).Astheclassicalresult,theorderofthesystemcanbereduced…
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LIE GROUPS ADMITTED BY AUTONOMOUS SYSTEM WITH GIVEN STRUCTURE CONSTANTS |
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| LeiJinzhi.LIE GROUPS ADMITTED BY AUTONOMOUSSYSTEM WITH GIVEN STRUCTURECONSTANTS[J].微分方程年刊(英文版),1999(3). |
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| Authors: | LeiJinzhi |
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| Abstract: | This paper study the Lie groups admitted by differential equations. It is proved in this paper that for any n-th order autonomous system and any given structure constants Ckij, the system admits n-1 local one parameter Lie groups, and the "non-trivial" structure constants of the Lie module generated by infinitesimal generators of these Lie groups are just Ckij. This result shows that integrable system may admit unsolvable local Lie group. |
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| Keywords: | autonomous system structure constant Lie group |
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