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TitleEquivalence of differential equations of order one
Author(s) Christophe Jermann, L.X. Chau Ngo, K.A. Nguyen, Maarten H. van der Vlerk
TypeArticle in Journal
AbstractAbstract The notion of strict equivalence for order one differential equations of the form f ( y ' , y , z ) = 0 with coefficients in a finite extension K of C ( z ) is introduced. The equation gives rise to a curve X over K and a derivation D on its function field K ( X ) . Procedures are described for testing strict equivalence, strict equivalence to an autonomous equation, computing algebraic solutions and verifying the Painlevé property. These procedures use known algorithms for isomorphisms of curves over an algebraically closed field of characteristic zero, the Risch algorithm and computation of algebraic solutions. The most involved cases concern curves X of genus 0 or 1. This paper complements work of M. Matsuda and of G. Muntingh & M. van der Put.
KeywordsOrdinary differential equations, Algebraic curves, Local behavior of solutions, Normal forms, Painlevé property, Algebraic solutions
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717114001096
LanguageEnglish
JournalJournal of Symbolic Computation
Volume71
Number0
Pages47 - 59
Year2015
Edition0
Translation No
Refereed No
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