English

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)

R2 v1 2026-06-28T22:03:33.907Z