Rational general solutions of higher order algebraic odes
Rational general solutions of higher order algebraic odes
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DOI：
10.1007/s11424-013-1252-0
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发表时间：
2013-03
影响因子：
2.1
通讯作者：
Yanli Huang;L. Ngô;F. Winkler
中科院分区：
文献类型：
--
作者：
Yanli Huang;L. Ngô;F. Winkler
本文将Ngô和Winkler（2010, 2011）求一阶非自治代数常微分方程（AODE）有理通解的方法推广到高阶AODE，并给出了其解超曲面的适当参数化。将求高阶AODE的有理通解问题简化为求关联系统的有理通解问题。原AODE及其关联系统的有理通解是可计算的1-1对应关系。通过对不变代数空间曲线进行适当的再参数化，给出了关联系统有合理解的充分必要条件。作者还将不变空间曲线与第一积分联系起来，并用有理第一积分来表征合理可解系统。
This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.