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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
39/2009

Higher-order Abel equations: Lagrangian formalism, Darboux polynomials and constants of the motion

José Cariñena, Partha Guha and Manuel Rañada

Abstract

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and it is proved the existence of two alternative Lagrangian formulations, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These higher-order Abel equations are studied by means of their Darboux polynomials and Jacobi multipliers. In all the cases a family of constants of the motion is explicitly obtained. The general $n$-dimensional case is also studied.

Received:
Jul 23, 2009
Published:
Jul 24, 2009
MSC Codes:
34A26, 34A34, 70H03
PACS:
02.30.Hq, 45.20.Jj
Keywords:
Higher-order Riccati equations, Darboux polynomials, Jacobi multipliers

Related publications

inJournal
2009 Repository Open Access
Jose F. Carinena, Partha Guha and Manuel F. Ranada

Higher-order Abel equations : Lagrangian formalism, first integrals and Darboux polynomials

In: Nonlinearity, 22 (2009) 12, pp. 2953-2969