Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 051, 11 pages      arXiv:1006.2891      https://doi.org/10.3842/SIGMA.2010.051

Linearization of Second-Order 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 second-order 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 second-order 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 second-order ordinary differential equations.

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References

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