RATIONAL GENERAL SOLUTIONS OF HIGHER ORDER ALGEBRAIC ODES

作     者：HUANG Yanli NG L X Chu WINKLER Franz 

作者机构：School of Computer Science and Software EngineeringTianjin Polytechnic University Research Institute for Symbolic Computation(RISC)Johannes Kepler University Department of MathematicsQuy Nhon University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2013年第26卷第2期

页      面：261-280页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

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 

主　　题：微分方程解 代数 高阶 一般解 空间曲线 重新参数化 充分条件 首次积分 

摘      要：This paper generalizes the method of Ngo 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.