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2009 Nonlinearity 22 2953-2969 doi: 10.1088/0951-7715/22/12/008
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Recommended by A S Fokas
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.
Mathematics Subject Classification: 34A26, 34A34, 34C14, 37J05, 70H03, 70H33
PACS numbers: 02.30.Hq, 45.20.Jj
Print publication: Issue 12 (December 2009) |
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