Birational transformations preserving rational solutions of algebraic ordinary differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:286

Article

Ngo, L. X. C.¹  Sendra, J. R.²  Winkler, F.³ 

[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

关键词: Algebraic differential equation;    Rational solution;    Integral birational transformation;    Integral curve;    Rational parametrization;   

DOI  :  10.1016/j.cam.2015.03.007

来源: Elsevier

【 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.

【 授权许可】

Free