On the reduction of non-linear oscillator-equations to Abel forms

摘要

The particular ordinary differential equations (ODEs) governing some specific non-linear oscillators are reduced to equivalent Abel equations by means of a series of functional transformations. These equivalent equations do not accept analytical solutions in terms of tabulated functions. So, the results of this work combined with the non-existence of exact solutions in the literature lead to the speculation that we need to construct new analytical functions in order to confront particular non-linearities in mechanical oscillations and physical problems generally.