Integrable Abel equations and Vein's Abel equation
Stefan C. Mancas, Haret C Rosu

TL;DR
This paper advances the understanding of Abel equations by reformulating key integrability results, applying them to Vein's Abel equation, and analyzing its solutions and phase space behavior.
Contribution
It introduces new findings in Abel equation integrability and applies these to Vein's Abel equation, expressing solutions via third order hyperbolic functions.
Findings
New integrability results for Abel equations
Explicit solutions of Vein's Abel equation using hyperbolic functions
Phase space analysis of the nonlinear oscillator
Abstract
We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
