134 citations · 918 across the 58 of their papers we have counts for
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Classification of scalar third order ordinary differential equations linearizable via generalized contact transformations
Hina M. Dutt, Asghar Qadir
Whereas Lie had linearized scalar second order ordinary differential equations (ODEs) by point transformations and later Chern had extended to the third order by using contact tran…
Linearization from complex Lie point transformations
Sajid Ali, Muhammad Safdar, Asghar Qadir
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension ,…
Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms
Hina M. Dutt, Asghar Qadir
Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing f…
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 of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis
Muhammad Safdar, Asghar Qadir, Sajid Ali
Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of var…
On the symmetry solutions of two-dimensional systems not solvable by standard symmetry analysis
Sajid Ali, Asghar Qadir, Muhammad Safdar
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. Th…
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…
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…
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…