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arXiv · 0912.2842

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

José F. Cariñena·Partha Guha·Manuel F. Rañada
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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.

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José F. Cariñena, Partha Guha, Manuel F. Rañada. 2009-12-15. Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials. https://doi.org/10.1088/0951-7715%2F22%2F12%2F008

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