Methods for exact solutions of nonlinear ordinary differential equations\
Exactly Solvable and Integrable Systems
2025-03-04 v1 Mathematical Physics
math.MP
Abstract
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by Eremenko, which can be turned into algorithms, thus avoiding \textit{ad hoc} assumptions, able to provide \textit{all} (as opposed to some) solutions in a precise class. To illustrate these methods, we present some new such exact solutions, physically relevent.
Keywords
Cite
@article{arxiv.2503.00834,
title = {Methods for exact solutions of nonlinear ordinary differential equations\},
author = {Robert Conte and Micheline Musette and Tuen Wai Ng and Chengfa Wu},
journal= {arXiv preprint arXiv:2503.00834},
year = {2025}
}
Comments
11 pages, 1 figure, to appear, Advances in mathematics (China)