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This article is cited in 19 scientific papers (total in 19 papers)
Geometric Linearization of Ordinary Differential Equations
Asghar Qadir Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Abstract:
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear
ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable equations and even on systems of equations. However, little has been done in the way of providing explicit criteria to determine their linearizability. Using the connection between isometries and symmetries of the system of geodesic equations criteria were established for second order quadratically and
cubically semi-linear equations and for systems of equations. The connection was proved for maximally symmetric spaces and a conjecture was put forward for other cases. Here the criteria are briefly reviewed and the conjecture is proved.
Keywords:
differential equations; geodesics; geometry; linearizability; linearization.
Received: August 13, 2007; in final form October 19, 2007; Published online November 6, 2007
Citation:
Asghar Qadir, “Geometric Linearization of Ordinary Differential Equations”, SIGMA, 3 (2007), 103, 7 pp.
Linking options:
https://www.mathnet.ru/eng/sigma229 https://www.mathnet.ru/eng/sigma/v3/p103
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Abstract page: | 384 | Full-text PDF : | 60 | References: | 25 |
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