Conditional linearization of the quintic nonlinear beam equation

Advances in Difference Equations

Waraporn Chatanin¹  Nuntawan Sripana² 

[1] Department of Mathematics, Faculty of Science, King Mongkut’Faculty of Liberal Arts, Rajamangala University of Technology Tawan-Ok Chakrabongse Bhuvanarth Campus, Bangkok, Thailand;s University of Technology Thonburi, Bangkok, Thailand

关键词: conditional linearization;    quintic nonlinear beam equation;    nonlinear ordinary differential equations;   

DOI  :  10.1186/s13662-017-1179-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY