A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms

TL;DR

This paper introduces an algorithmic method to find point transformations that convert scalar ODEs with three-dimensional symmetry algebras into their canonical forms, simplifying their analysis.

Contribution

It presents a novel algorithmic approach specifically for scalar ODEs with three-dimensional symmetry algebras to systematically obtain their canonical forms.

Findings

Successfully constructs point transformations for targeted ODEs.

Simplifies the process of classifying ODEs based on symmetry.

Enhances the understanding of symmetry-based reduction methods.

Abstract

We provide an algorithmic approach to the construction of point transformations for scalar ordinary differential equations that admit three-dimensional symmetry algebras which lead to their respective canonical forms.