Linearization of fourth order ordinary differential equations by point transformations
|Document type:||Journal Articles|
|Article type:||Original article|
|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|
|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:||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.
|Keywords:||linearization of differential equations, contact transformations, Lie group analysis|