Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations
General Mathematics
2026-02-17 v1
Abstract
Cartan's equivalence method is applied to explicitly construct invariant coframes for four branches, which are used to characterize all non-linearizable third-order ODEs with a four-dimensional Lie symmetry subalgebra under point transformations. Additionally, we present a method for constructing the point transformations based on the derived invariant coframes. Examples are provided to illustrate our approach.
Cite
@article{arxiv.2602.13317,
title = {Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations},
author = {Omar A. Abuloha and Marwan Aloqeili and Ahmad Y. Al-Dweik and F. M. Mahomed},
journal= {arXiv preprint arXiv:2602.13317},
year = {2026}
}