Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations

• Main Authors: Warisa Nakpim, Sergey V. Meleshko
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2010-06-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: linearization problem; generalized Sundman transformations; nonlinear second-order ordinary differential equations
• Online Access: http://dx.doi.org/10.3842/SIGMA.2010.051

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.