Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
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Publication:3652643
DOI10.1088/0951-7715/22/12/008zbMath1188.34008arXiv0912.2842OpenAlexW2041048420MaRDI QIDQ3652643
José F. Cariñena, Partha Guha, Manuel F. Rañada
Publication date: 15 December 2009
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0912.2842
Riccati equationsLagrangian formalismDarboux polynomialsfirst integralsAbel equationsJacobi multipliers
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Equivalence classes and linearization of the Riccati and Abel chain ⋮ Geometric approach to dynamics obtained by deformation of Lagrangians ⋮ Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains ⋮ Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of Ermakov-Pinney Lie algebra ⋮ Folding transformations of equations from the Gambier family ⋮ A geometric approach to integrability of Abel differential equations ⋮ A nonlocal connection between certain linear and nonlinear ordinary differential equations: Extension to coupled equations ⋮ Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
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