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| Properties of Rational General Solutions for First Order Multivariate Autonomous Rational Differential Systems |
| Yanli Huang, Beibei Xu, Xiaoliang Li |
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Abstract This paper studies the properties of rational general solutions for first
order multivariate autonomous rational differential systems. We
obtain a necessary and sufficient conditions for existence of
rational general solution of first order multivariate autonomous
rational differential system if the degree bound of rational
solutions of this system is given. Due to the problem for computing
a rational solution of the multivariate rational differential system
can be reduced to finding a linear rational solution of an
autonomous differential equation, we also prove that the linear
rational solvability of the resulting autonomous differential
equation does not depend on the choice of proper parametrizations of
invariant algebraic space curves. In addition, two different
rational solutions corresponding to the same invariant algebraic
space curve are proved to be related by a shifting of the variable.
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| DOI:10.12733/jics20105672 |
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