Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415083384
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