Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations

Omar A. Abuloha; Marwan Aloqeili; Ahmad Y. Al-Dweik; F. M. Mahomed

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arXiv · 2602.13317

Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations

Omar A. Abuloha·Marwan Aloqeili·Ahmad Y. Al-Dweik·F. M. Mahomed

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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.

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BibTeX RIS

Omar A. Abuloha, Marwan Aloqeili, Ahmad Y. Al-Dweik, F. M. Mahomed. 2026-02-10. Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations. https://arxiv.org/abs/2602.13317

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