48 citations · 232 across the 26 of their papers we have counts for
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On Computing Linearizing Coordinates From Symmetry Algebra
Sajid Ali, Hassan Azad, Said Waqas Shah +1
A characterization of the symmetry algebra of the th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is u…
Linearization of third-order ordinary differential equations u'''=f(x,u,u',u'') via point transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, F. M. Mahomed +1
The linearization problem by use of the Cartan equivalence method for scalar third-order ODEs via point transformations was solved partially in [1,2]. In order to solve this proble…
Invariant characterization of third-order ODEs that admit a five-dimensional point symmetry Lie algebra
Ahmad Y. Al-Dweik, M. T. Mustafa, F. M. Mahomed
The Cartan equivalence method is applied to provide an invariant characterization of the third-order ordinary differential equation which admits a five-dimensi…
Invariants of third-order ordinary differential equations via fiber preserving transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, H. Azad +1
Bagderina \cite{Bagderina2008} solved the equivalence problem for scalar third-order ordinary differential equations (ODEs), quadratic in the second-order derivative, via point tra…
Invariants for systems of two linear hyperbolic-type equations by complex methods
A. Aslam, M. Safdar, F. M. Mahomed
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real inf…
-symmetry criteria for linearization of second order ODEs via point transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, Raed A. Mara'beh +1
An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between -symmetries and first integrals. This relation fur…
A characterization of iterative equations by their coefficients
J. C. Ndogmo, F. M. Mahomed
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations i…
Higher Dimensional Systems of Differential Equations Obtained by Iterative Use of Complex Methods
F M Mahomed, Asghar Qadir
Systems of two ordinary and partial differential equations (ODEs and PDEs) had been obtained from a scalar complex ODE by splitting it into its real and imaginary parts. The proced…
Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods
S. Ali, F. M. Mahomed, Asghar Qadir
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometr…
Two-dimensional Systems that Arise from the Noether Classification of Lagrangians on the Line
M. U. Farooq, S. Ali, Fazal M. Mahomed
The Noether-like operators that play an essential role in writing down the invariants for systems of two ordinary differential equations (ODEs) are constructed. The classification…
Conditional Linearizability Criteria for Scalar Fourth Order Semi-Linear Ordinary Differential Equations
F. M. Mahomed, A. Qadir
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential…
Conditional linearizability criteria for a system of third-order ordinary differential equations
F. M. Mahomed, I. Naeem, Asghar Qadir
We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by different…
Invariant Linearization Criteria for Systems of Cubically Semi-Linear Second-Order Ordinary Differential Equations
F. M. Mahomed, Asghar Qadir
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations ar…
Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations
S. Ali, F. M. Mahomed, Asghar Qadir
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that…
Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - I: Ordinary Differential Equations
S. Ali, F. M. Mahomed, Asghar Qadir
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is us…