Birational transformations preserving rational solutions of algebraic ordinary differential equations

被引：9

作者：

Ngo, L. X. C. ^{[1
]}

Sendra, J. R. ^{[2
]}

Winkler, F. ^{[3
]}

机构：

[1] Quy Nhon Univ, Dept Math, Quy Nhon, Vietnam

[2] Univ Alcala, Dept Fis & Matemat, E-28871 Madrid, Spain

[3] Johannes Kepler Univ Linz, RISC, A-4040 Linz, Austria

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 286卷

基金：

奥地利科学基金会;

关键词：

Algebraic differential equation; Rational solution; Integral birational transformation; Integral curve; Rational parametrization; GENERAL-SOLUTIONS; SYSTEMS;

D O I：

10.1016/j.cam.2015.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the set of all rational transformations with the property of preserving the existence of rational solutions of algebraic ordinary differential equations (AODEs). This set is a group under composition and, by its action, partitions the set of AODEs into equivalence classes for which the existence of rational solutions is an invariant property. Moreover, we describe how the rational solutions, if any, of two different AODEs in the same class are related. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：114 / 127

页数：14

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