
SIGMA 3 (2007), 103, 7 pages arXiv:0711.0814
http://dx.doi.org/10.3842/SIGMA.2007.103
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
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
Received August 13, 2007, in final form October 19, 2007; Published online November 06, 2007;
References [17−21] updated November 11, 2007
Abstract
The linearizability of differential equations was
first considered by Lie for scalar second order semilinear
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 semilinear 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.
Key words:
differential equations; geodesics; geometry; linearizability; linearization.
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