Symmetry, Equivalence and Integrable Classes of Abel Equations

2004/04/09 by V. Boyko, Vyacheslav M. Boyko, Boyko, Vyacheslav M. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0404020

8 pages, essentially revised and extended version

arxiv created 2005/07/04 · arxiv updated 2009/12/01

Abstract

We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary differential equations. The problem of linearizability of the equations under consideration is discussed.

Citations

• Linearisable third order ordinary differential equations and generalised Sundman transformations

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• The damped Pinney equation and its applications to dissipative quantum mechanics

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