arXiv subjects

Marwan Aloqeili

Publications and source records attributed to Marwan Aloqeili.

5 recordsLinked to original sources

arXiv2026

Invariant characterization of scalar third-order ODEs that admit the maximal contact symmetry Lie algebra

The Cartan equivalence method is utilized to deduce an invariant characterization of the scalar third-order ordinary differential equation $u'''=f(x,u,u',u'')$ which admits the maximal ten-dimensional contact symmetry Lie algebra. The method provides auxiliary functions which can be used to efficiently determine the contact transformation that does the reduction to the simplest linear equation $\bar{u}'''=0$. Furthermore, ample examples are given to illustrate our method.

math.CA↗

arXiv2026

Linearization Problem for a System of Two Second-Order ODEs via Cartan's Method: Branch I

Cartan's method classifies the class of linearizable system of two second-order ODEs into many branches. This paper investigates Branch I of the classification, characterized by a rank-one generalized Wilczynski invariant matrix and the vanishing of two relative invariants $K_1$ and $L_1$. It is demonstrated that any linearizable system belonging to this branch admits an eight-dimensional Lie point symmetry algebra. The canonical form for this class is provided and the invariant characterizations based on the obtained rank-zero invariant coframe and the corresponding constant structure equations are established. Also, a systematic procedure for constructing the linearizing point transformation is derived. The theoretical results are illustrated by several examples.

math.GM↗

arXiv2026

Linearization Problem for Third-Order ODEs with Four- and Five-Dimensional Lie Symmetry Algebras under Contact Transformations

Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras, respectively. A procedure for deriving the corresponding contact transformations is also presented, along with illustrative examples.

math.GM↗

arXiv2026

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

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.

math.GM↗

arXiv2026

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

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.

math.GM↗