Conditional linearization of the quintic nonlinear beam equation
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Publication Details
Author list: Sripana N., Chatanin W.
Publisher: SpringerOpen
Publication year: 2017
Journal: Advances in Difference Equations (1687-1839)
Volume number: 2017
Issue number: 1
ISSN: 1687-1839
eISSN: 1687-1847
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, the linearization of third-order ordinary differential equations, which are the transformed equations of the quintic nonlinear beam equation, is presented. First of all, a third-order ordinary differential equation can be linearized if its coefficients satisfied the conditions of the linearization theorem. So, the conditions for linearization are investigated. After that, in each case, the linearizing transformation is defined, and finally the linear third-order equation is obtained. Moreover, after calculating the solutions to linear third-order equations and substituting the original variables to the solutions, the exact solutions to the equation of motion are obtained. ฉ 2017, The Author(s).
Keywords
conditional linearization, nonlinear ordinary differential equations, quintic nonlinear beam equation
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