Linearization of fourth order ordinary differential equations by point transformations
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Nail H. Ibragimov, Sergey Meleshko, Supaporn Suksern |
| Title: | Linearization of fourth order ordinary differential equations by point transformations |
| Journal: | Journal of Physics A: Mathematical and Theoretical |
| Year: | 2008 |
| Volume: | 23 |
| Issue: | 41 |
| Pagination: | 206-235 |
| ISSN: | 1751-8113 |
| Publisher: | IOP Publishers |
| Organization: | Blekinge Institute of Technology |
| Department: | School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap) School of Engineering S- 371 79 Karlskrona +46 455 38 50 00 http://www.tek.bth.se/ |
| Authors e-mail: | nib@bth.se |
| Language: | English |
| Abstract: | A general methodology for linearization of fourth order ordinary differential equations is developed using point transformations. The solution of the problem on linearization of fourth-order equations by means of point transformations is presented here. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of equations which is linear in the third-order derivative. We provide the linearization test and describe the procedure for obtaining the linearizing transformations as well as the linearized equation. For ordinary differential equations of order greater than 4 we obtain necessary conditions, which separate all linearizable equations into two classes. |
| Subject: | Mathematics\Analysis Mathematics\General |
| Keywords: | linearization of differential equations, contact transformations, Lie group analysis |
