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MiS Preprint

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

José Cariñena, Partha Guha and Manuel Rañada


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.

MSC Codes:
34A26, 34A34, 70H03
02.30.Hq, 45.20.Jj
Higher-order Riccati equations, Darboux polynomials, Jacobi multipliers

Related publications

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