Transforming Radical Differential Equations to Algebraic Differential Equations

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 vari...

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2024-05, Vol.21 (3), Article 87
Main Authors: Falkensteiner, Sebastian, Sendra, J. Rafael
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Mathematics and Statistics
Partial differential equations
Polynomials
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-024-02624-1