On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
|
|
| Creator |
Mustafa, M.T.
Al-Dweik, A.Y. Mara'beh, R.A. |
|
| Description |
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.
|
|
| Date |
2019-02-19T18:28:46Z
2019-02-19T18:28:46Z 2013 |
|
| Type |
Article
|
|
| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 34A05; 34A25 DOI: http://dx.doi.org/10.3842/SIGMA.2013.041 http://dspace.nbuv.gov.ua/handle/123456789/149194 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|