Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-order Abel equations: Lagrangian formalism, first integrals and
  Darboux polynomials   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.

33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex