Rational general solutions of planar rational systems of autonomous ODEs

机译：自治ODE平面有理系统的有理通用解。

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摘要

In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case.

机译：在本文中，我们提供了一种算法，可以根据其有理不变代数曲线来计算自治常微分方程（ODE）有理系统的显式有理解。该方法基于这些曲线的合理有理参数化以及通过线性重新参数化可以找到给定ODEs系统的有理解的事实。此外，如果系统具有合理的第一积分，我们可以确定它是否具有合理的一般解，并在肯定的情况下对其进行计算。

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期刊名称 Elsevier Sponsored Documents
作者
L.X. Châu Ngô; Franz Winkler;
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作者单位

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年(卷),期 -1(46),10-10
年度 -1
页码 1173–1186
总页数 10
原文格式 PDF
正文语种
中图分类
关键词
Ordinary differential equations Rational solutions Invariant algebraic curves Rational parametrizations Rational first integrals;

机译：常微分方程;有理解;不变代数曲线;有理参数化;有理一阶积分;

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1. Rational general solutions of planar rational systems of autonomous ODEs [J] . LX.Châu Ngô, Franz Winkler urnal of Symbolic Computation . 2011,第10期

机译：自治ODE平面有理系统的有理通用解。
2. Properties of Rational General Solutions for First Order Multivariate Autonomous Rational Differential Systems [J] . Yanli Huang, Beibei Xu, Xiaoliang Li Journal of information and computational science . 2015,第6期

机译：一阶多元自治有理微分系统的有理通用解的性质
3. Rational general solutions of first order non-autonomous parametrizable ODEs [J] . L.X. Chau Ngo, Franz Winkler Journal of symbolic computation . 2010,第12期

机译：一阶非自治可参数化ODE的有理通用解
4. Rational General Solutions of Trivariate Rational Systems of Autonomous ODEs [C] . Yanli Huang, L.X.Ch(a)u Ng(o), Franz Winkler Proceedings of the fourth international conference on mathematical Aspects of computer and information sciences. . 2011

机译：自治ODE的三元有理系统的有理通用解。
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Rational general solutions of planar rational systems of autonomous ODEs

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