On the integrable rational Abel differential equations

Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

In Cheb-Terrab and Roche (Comput Phys Commun 130(1-2):204-231, 2000) a classification of the Abel equations known as solvable in the literature was presented. In this paper, we show that all the integrable rational Abel differential equations that appear in Cheb-Terrab and Roche (Comput Phys Commun 130(1-2):204-231, 2000) and consequently in Cheb-Terrab and Roche (Eur J Appl Math 14(2):217-229, 2003) can be reduced to a Riccati differential equation or to a first-order linear differential equation through a change with a rational map. The change is given explicitly for each class. Moreover, we have found a unified way to find the rational map from the knowledge of the explicitly first integral. © 2009 Birkhäuser Verlag Basel/Switzerland.
Original languageEnglish
Pages (from-to)33-39
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume61
DOIs
Publication statusPublished - 1 Feb 2010

Keywords

  • Abel differential equation
  • First-order linear differential equation
  • Integrability
  • Riccati equation

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