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- Title
Linearizability of Nonlinear Second-Order Ordinary Differential Equations by Using a Generalized Linearizing Transformation.
- Authors
Voraka, Prakrong; Suksern, Supaporn; Donjiwprai, Nontakan
- Abstract
In this paper, we have proposed the linearization problem of second-order ordinary differential equation under the generalized linearizing transformation. We found the necessary form for reducing the second-order ordinary differential equation to simple linear equation. We also obtained sufficient condition for making the above form to be linear. Further, the procedure of linear transformation within the study is demonstrated in the explicit form. Moreover, we apply the obtained linearization criteria to the interesting problems of nonlinear ordinary differential equations and nonlinear partial differential equations, for examples the parachute equation, the Painlevé - Gambier XI equation, the equation for the variable frequency oscillator, the one-dimensional nonpolynomial oscillator, the equation that can be linearizable by point and Sundman transformations, the modified generalized Vakhnenko equation.
- Subjects
PARTIAL differential equations; LINEAR differential equations; NONLINEAR equations; LINEAR equations; ORDINARY differential equations; NONLINEAR differential equations
- Publication
IAENG International Journal of Applied Mathematics, 2020, Vol 50, Issue 4, p845
- ISSN
1992-9978
- Publication type
Article