
SIGMA 6 (2010), 051, 11 pages arXiv:1006.2891
https://doi.org/10.3842/SIGMA.2010.051
Linearization of SecondOrder Ordinary Differential Equations by Generalized Sundman Transformations
Warisa Nakpim and Sergey V. Meleshko
School of Mathematics, Institute of Science, Suranaree University of
Technology, Nakhon Ratchasima, 30000, Thailand
Received January 18, 2010, in final form June 03, 2010; Published online June 15, 2010
Abstract
The linearization problem of a secondorder ordinary differential
equation by the generalized Sundman transformation was considered
earlier by Duarte, Moreira and Santos using the Laguerre form.
The results obtained in the present paper demonstrate that their
solution of the linearization problem for a secondorder ordinary
differential equation via the generalized Sundman transformation
is not complete. We also give examples which show that the
Laguerre form is not sufficient for the linearization problem via
the generalized Sundman transformation.
Key words:
linearization problem; generalized Sundman transformations; nonlinear secondorder ordinary differential equations.
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