388 research outputs found
Conditional linearizability criteria for a system of third-order ordinary differential equations
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 differentiating a system of second-order quadratically
semi-linear ODEs and using the original system to replace the second
derivative. The procedure developed splits into two cases, those where the
coefficients are constant and those where they are variables. Both cases are
discussed and examples given
A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms
We provide an algorithmic approach to the construction of point
transformations for scalar ordinary differential equations that admit
three-dimensional symmetry algebras which lead to their respective canonical
forms
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