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This article is cited in 8 scientific papers (total in 8 papers)
On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
M. Tahir Mustafa, Ahmad Y. Al-Dweik, Raed A. Mara'beh Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Abstract:
The linearization problem for nonlinear second-order ODEs to the Laguerre form by means of generalized Sundman transformations (S-transformations) is considered, which has been investigated by Duarte et al. earlier. A characterization of these S-linearizable equations in terms of first integral and procedure for construction of linearizing S-transformations has been given recently by Muriel and Romero. Here we give a new characterization of S-linearizable equations in terms of the coefficients of ODE and one auxiliary function. This new criterion is used to obtain the general solutions for the first integral explicitly, providing a direct alternative procedure for constructing the first integrals and Sundman transformations. The effectiveness of this approach is demonstrated by applying it to find the general solution for geodesics on surfaces of revolution of constant curvature in a unified manner.
Keywords:
linearization problem; generalized Sundman transformations; first integrals; nonlinear second-order ODEs.
Received: February 16, 2013; in final form May 25, 2013; Published online May 31, 2013
Citation:
M. Tahir Mustafa, Ahmad Y. Al-Dweik, Raed A. Mara'beh, “On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations”, SIGMA, 9 (2013), 041, 10 pp.
Linking options:
https://www.mathnet.ru/eng/sigma824 https://www.mathnet.ru/eng/sigma/v9/p41
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Abstract page: | 393 | Full-text PDF : | 37 | References: | 26 |
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