Linearization of third-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
Title: Linearization of third-order ordinary differential equations by point transformations.
Translated title: Linearization of third-order ordinary differential equations by point transformations.
Journal: Archives of ALGA
Year: 2004
Volume: 1
Pagination: 95-126
ISSN: 1652-4934
Publisher: ALGA publications, BTH
City: Karlskrona; Sweden
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: We present here the necessary and sufficient conditions for linearization of third-order equations by means of point transformations.
We show that all third-order equations that are linearizable by point transformations are contained either in the class of equations which are linear in the second-order derivative, or in the class of equations which are quadratic in the second-order derivative. We provide the linearization test for each of these classes and describe the procedure for obtaining the linearizing point transformations as well as the linearized equation.
Subject: Mathematics\Analysis
Keywords: linearization of third-order equations, point transformations, symmetries
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