Transforming Radical Differential Equations to Algebraic Differential Equations
Classical Analysis and ODEs
2024-04-23 v4 Algebraic Geometry
Analysis of PDEs
Abstract
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations among them by means of a rational change of variables. The solutions of the given equation and its transformation correspond one-to-one. This work can be seen as a generalization of previous work on reparametrization of ODEs and PDEs with radical coefficients.
Cite
@article{arxiv.2112.00994,
title = {Transforming Radical Differential Equations to Algebraic Differential Equations},
author = {Sebastian Falkensteiner and Rafael Sendra},
journal= {arXiv preprint arXiv:2112.00994},
year = {2024}
}