Linearization of third-order ordinary differential equations by point transformations.
|Document type:||Journal Articles|
|Article type:||Original article|
|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|
|Publisher:||ALGA publications, BTH|
|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
|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.
|Keywords:||linearization of third-order equations, point transformations, symmetries|