Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
Інший ID:
2010 Mathematics Subject Classification: 34A05; 34A25
DOI: http://dx.doi.org/10.3842/SIGMA.2013.041
DOI: http://dx.doi.org/10.3842/SIGMA.2013.041
Посилання:
On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations / M.T. Mustafa, A.Y. Al-Dweik, R.A. Mara'beh // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 18 назв. — англ.
Підтримка:
The authors would like to thank the King Fahd University of Petroleum and Minerals for its
support and excellent research facilities. They also thank the reviewers for their comments which
have considerably improved the paper.
Дата:
2013
Переглядів:
554
Завантажень:
246
Анотація:
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.
