Equivalence Problem for Non-Linearizable Fourth-Order ODEs with Five-Dimensional Lie Symmetry subalgebra via Inductive Cartan Equivalence Method

TL;DR

This paper develops a method using the Inductive Cartan equivalence approach to classify and transform certain fourth-order ODEs with five-dimensional Lie symmetry subalgebras.

Contribution

It explicitly constructs invariant coframes and provides a procedure to find point transformations for non-linearizable fourth-order ODEs.

Findings

Constructed four invariant 1-form coframes for different branches.

Characterized non-linearizable fourth-order ODEs with five-point symmetry subalgebras.

Demonstrated the transformation procedure through examples.

Abstract

Four coframes of invariant 1-forms are explicitly constructed using the Inductive Cartan equivalence method with rank zero corresponding to four distinct branches. These coframes are employed to characterize non-linearizable fourth-order ODEs under point transformation with a five-point symmetry Lie subalgebra. Moreover, we propose a procedure for obtaining the point transformation by using the derived invariant coframes, demonstrated through examples.