RATIONAL GENERAL SOLUTIONS OF HIGHER ORDER ALGEBRAIC ODES  

作　　者：HUANG Yanli NG L X Chu WINKLER Franz 

机构地区：[1]School of Computer Science and Software Engineering,Tianjin Polytechnic University [2]Research Institute for Symbolic Computation(RISC),Johannes Kepler University [3]Department of Mathematics,Quy Nhon University

出　　处：《Journal of Systems Science & Complexity》2013年第2期261-280,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the Austrian Science Foundation(FWF) via the Doctoral Program "Computational Mathematics" under Grant No.W1214;Project DK11,the Project DIFFOP under Grant No.P20336-N18;the SKLSDE Open Fund SKLSDE-2011KF-02;the National Natural Science Foundation of China under Grant No.61173032;the Natural Science Foundation of Beijing under Grant No.1102026,and the China Scholarship Council

摘　　要：This paper generalizes the method of Ng6 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.

关 键 词：Algebraic ODE associated system invariant algebraic space curve rational first integral rational general solution. 

分 类 号：O175[理学—数学]