José F Cariñena et al 2009 Nonlinearity 22 2953 doi:10.1088/0951-7715/22/12/008
José F Cariñena1, Partha Guha2,3 and Manuel F Rañada1
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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.
02.10.De Algebraic structures and number theory
02.40.-k Geometry, differential geometry, and topology
34A34 Nonlinear equations and systems, general
37J05 General theory, relations with symplectic geometry and topology
Issue 12 (December 2009)
Received 15 April 2009, in final form 12 October 2009
Published 30 October 2009
José F Cariñena et al 2009 Nonlinearity 22 2953
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