Linearization from Complex Lie Point Transformations
TL;DR: A geometrical construction of the procedure adopted that provides an analogue in of the linearizability criteria in .
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Abstract: 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 , with . We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in of the linearizability criteria in .
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Citations
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Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations
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References
•Book
Applications of Lie Groups to Differential Equations
Peter J. Olver
- 01 Jan 1986
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
9K
•Book
Elementary Lie Group Analysis and Ordinary Differential Equations
N. Kh. Ibragimov
- 23 Mar 1999
TL;DR: In this paper, the authors present a Lie Group Analysis of Ordinary Differential Equations (ODE) for the first order and second order differential equations, respectively, and integrate them into Third Order Equations.
923
Invariant linearization criteria for systems of cubically nonlinear second-order ordinary differential equations
Fazal M. Mahomed,Asghar Qadir +1 more
TL;DR: In this article, it is shown that there are two branches for the linearization problem via point transformations for an arbitrary system of second-order ODEs and its reduction to the simplest system.
On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations
TL;DR: In this article, a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method is introduced, where the integrals of motion associated with the given equation are deduced, so that the general solution follows straightforwardly from these integrals.
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Characterization of the Newtonian Free Particle System in $m\geqslant 2$ Dependent Variables
TL;DR: In this paper, the problem of linearizability of a system of second-order ODEs was studied in the context of nonlinear Newtonian free particle systems, and a necessary and sufficient condition was given for the system to be equivalent under a point transformation.
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