Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
Mathematical Physics
2015-05-14 v1 math.MP
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 the existence of two alternative Lagrangian formulations is proved, 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.
Cite
@article{arxiv.0912.2842,
title = {Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials},
author = {José F. Cariñena and Partha Guha and Manuel F. Rañada},
journal= {arXiv preprint arXiv:0912.2842},
year = {2015}
}