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| Content Provider | Springer Nature Link |
|---|---|
| Author | Huang, Yanli Ngô, L. X. Châu Winkler, Franz |
| Copyright Year | 2013 |
| Abstract | 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. |
| Starting Page | 261 |
| Ending Page | 280 |
| Page Count | 20 |
| File Format | |
| ISSN | 10096124 |
| Journal | Journal of Systems Science and Complexity |
| Volume Number | 26 |
| Issue Number | 2 |
| e-ISSN | 15597067 |
| Language | English |
| Publisher | Academy of Mathematics and Systems Science, Chinese Academy of Sciences |
| Publisher Date | 2013-03-01 |
| Publisher Place | Beijing |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Algebraic ODE associated system invariant algebraic space curve rational first integral rational general solution Systems Theory, Control Operations Research/Decision Theory Mathematics of Computing Statistical Physics, Dynamical Systems and Complexity Statistics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Information Systems |
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