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
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